user18029: A famous recent example of this ending happened last year between Carlsen and Firouzja. 
Here, Firouzja time ran out, so Carlsen won
[Title "Alireza Firouzja-Magnus Carlsen, World Blitz Championship, Moscow Russia, 12/30/2019"]
[FEN ""]
[startply "132"]

1. e4 e5 2. Nf3 Nc6 3. Bb5 a6 4. Ba4 d6 5. O-O Bd7 6. c3 g6 7. d4 Bg7 8. h3 Nf6 9. Bc2 O-O 10. Re1 Re8 11. Nbd2 Qe7 12. Nf1 Qf8 13. Ng3 Bh6 14. Ng5 Nd8 15. Bb3 Ne6 16. h4 Rad8 17. Be3 Bg7 18. h5 Bh6 19. Qc1 Ng4 20. Nxe6 fxe6 21. Rf1 Nxe3 22. fxe3 Qe7 23. hxg6 hxg6 24. Qd2 exd4 25. cxd4 Kg7 26. Rf3 Rf8 27. Raf1 Rxf3 28. Rxf3 Rf8 29. Qc3 c6 30. Nf1 e5 31. Rxf8 Kxf8 32. Qc4 Qf6 33. dxe5 dxe5 34. Qb4+ c5 35. Qxb7 Bb5 36. Qc8+ Ke7 37. Qxc5+ Qd6 38. Qxd6+ Kxd6 39. Bf7 Bxf1 40. Kxf1 g5 41. Ke2 Bf8 42. Kf3 Ke7 43. Bc4 a5 44. Ke2 Kd6 45. Bd5 Be7 46. Kf3 Bd8 47. Kg4 Be7 48. Kf5 Bd8 49. g4 Be7 50. a3 Bd8 51. b4 axb4 52. axb4 Be7 53. b5 Bd8 54. Kg6 Kc5 55. Kf5 Kxb5 56. Kxe5 Kc5 57. Ke6 Ba5 58. e5 Bd2 59. e4 Bc3 60. Kf5 Kb6 61. e6 Kc7 62. Kg6 Kd8 63. Kxg5 Ke7 64. Kh5 Bd2 65. g5 Bf4 66. Kg4 Bd2

In that tournament, the arbiter ruled that Carlsen wins since the he (technically) had sufficient mating material (a King+Bishop, and  Firouzja had >=1 piece in addition to their King). There is a concise explanation here (from 10m 42s)
Question
Does this rule stand in majorchess tournaments? Or is there some special rule to cover this situation and override the idea that King + Bishop is sufficient for checkmate if the opponent has at least one piece in addition to their king?
Note
Some (possibly in/correct) answers here state that the rules of chess deem such a situation to not have sufficient mating material. I am not sure how reliable they are.

user15783: Here's an example of a "possible series of moves" from FIDE rules 9.6, so White can technically (despite nearly impossible in reality) be checkmated:
[FEN "8/4k3/4P3/3B2P1/4P1K1/8/3b4/8 w - - 3 67"]
[startply "0"]

67. Kh5 Kf8 68. Kh6 Bb4 69. Kh7 Bd6 70. e5 Bxe5 71. Be4 Bd6 72. Kh8 Ba3 73. Bh7 Bb2#


user4418: 
Does this rule stand in major Chess tournaments?

This rule applies in all tournaments where FIDE Laws of Chess take precedence. So, yes, it applies in all major tournaments including USCF and all federations which are affiliated to FIDE.
If it appears to not work on a particular website then that is likely a bug on the platform and it is worth reporting to the platform.

Some (possibly in/correct) answers here state that the rules of
  chess deem such a situation to not have sufficient mating material. I
  am not sure how reliable they are.

No, what you say is not correct. The question on the Quora website is not the same. It is asking about forced checkmate. If your flag falls then the opponent does not need enough material to be able to force checkmate. He only needs enough material to checkmate you with you making the worst possible moves. If that is possible then you lose on time. Only if there is no possible sequence of moves leading to checkmate do you get a draw. 

user19877: First, Carlsen, despite having only the Bishop, WON that game. So it is not about mating material, but about ANY possible mating position, and there was one here.
The rule at hand is this:

Paragraph 6.9 of the FIDE Laws of Chess state:
The game is drawn, if the position is such that the opponent cannot
  checkmate the player’s king by any possible series of legal moves.

There were positions that white could be mated, even though it required total cooperation, and there is no way that Firouzja would have allowed it. That was irrelevant, so it was a loss.
Also see this related question.
Here are the USCF rules.
14D. Insufficient material to continue.
The game is drawn when one of the following endings exists as of the most recently determined legal move, in which the possibility of a win is excluded for either side. 
14D1. King vs. king.
14D2. King vs. king with bishop or knight.
14D3. King and bishop vs. king and bishop, with both bishops on diagonals of the same color. 
14D4. No legal moves leading to checkmate by opponent. There are no legal moves that could lead to the player being checkmated by the opponent
So, even these rules are quite specific as to the material for an automatic draw.

18029: <p>A famous recent example of this ending happened last year <a href="https://www.chessgames.com/perl/chessgame?gid=1988510" rel="nofollow noreferrer">between</a> Carlsen and Firouzja. </p>

<p>Here, Firouzja time ran out, so Carlsen won</p>

<pre><code>[Title "Alireza Firouzja-Magnus Carlsen, World Blitz Championship, Moscow Russia, 12/30/2019"]
[FEN ""]
[startply "132"]

1. e4 e5 2. Nf3 Nc6 3. Bb5 a6 4. Ba4 d6 5. O-O Bd7 6. c3 g6 7. d4 Bg7 8. h3 Nf6 9. Bc2 O-O 10. Re1 Re8 11. Nbd2 Qe7 12. Nf1 Qf8 13. Ng3 Bh6 14. Ng5 Nd8 15. Bb3 Ne6 16. h4 Rad8 17. Be3 Bg7 18. h5 Bh6 19. Qc1 Ng4 20. Nxe6 fxe6 21. Rf1 Nxe3 22. fxe3 Qe7 23. hxg6 hxg6 24. Qd2 exd4 25. cxd4 Kg7 26. Rf3 Rf8 27. Raf1 Rxf3 28. Rxf3 Rf8 29. Qc3 c6 30. Nf1 e5 31. Rxf8 Kxf8 32. Qc4 Qf6 33. dxe5 dxe5 34. Qb4+ c5 35. Qxb7 Bb5 36. Qc8+ Ke7 37. Qxc5+ Qd6 38. Qxd6+ Kxd6 39. Bf7 Bxf1 40. Kxf1 g5 41. Ke2 Bf8 42. Kf3 Ke7 43. Bc4 a5 44. Ke2 Kd6 45. Bd5 Be7 46. Kf3 Bd8 47. Kg4 Be7 48. Kf5 Bd8 49. g4 Be7 50. a3 Bd8 51. b4 axb4 52. axb4 Be7 53. b5 Bd8 54. Kg6 Kc5 55. Kf5 Kxb5 56. Kxe5 Kc5 57. Ke6 Ba5 58. e5 Bd2 59. e4 Bc3 60. Kf5 Kb6 61. e6 Kc7 62. Kg6 Kd8 63. Kxg5 Ke7 64. Kh5 Bd2 65. g5 Bf4 66. Kg4 Bd2
</code></pre>

<p>In that tournament, the arbiter ruled that Carlsen wins since the he (technically) had sufficient mating material (a King+Bishop, and  Firouzja had >=1 piece in addition to their King). There is a concise explanation <a href="https://www.youtube.com/watch?v=AxKmO0SCNkc&amp;t=642s" rel="nofollow noreferrer">here</a> (from 10m 42s)</p>

<h3>Question</h3>

<p>Does this rule stand in majorchess tournaments? Or is there some special rule to cover this situation and override the idea that King + Bishop is sufficient for checkmate if the opponent has at least one piece in addition to their king?</p>

<h3>Note</h3>

<p>Some (possibly in/correct) answers <a href="https://www.quora.com/How-do-you-checkmate-with-a-king-and-a-bishop-how-does-the-strategy-works" rel="nofollow noreferrer">here</a> state that the rules of chess deem such a situation to <strong>not</strong> have sufficient mating material. I am not sure how reliable they are.</p>
 15783: <p>Here's an example of a "possible series of moves" from FIDE rules 9.6, so White can technically (despite nearly impossible in reality) be checkmated:</p>

<pre><code>[FEN "8/4k3/4P3/3B2P1/4P1K1/8/3b4/8 w - - 3 67"]
[startply "0"]

67. Kh5 Kf8 68. Kh6 Bb4 69. Kh7 Bd6 70. e5 Bxe5 71. Be4 Bd6 72. Kh8 Ba3 73. Bh7 Bb2#
</code></pre>
 4418: <blockquote>
  <p>Does this rule stand in major Chess tournaments?</p>
</blockquote>

<p>This rule applies in <em>all</em> tournaments where FIDE Laws of Chess take precedence. So, yes, it applies in all major tournaments including USCF and all federations which are affiliated to FIDE.</p>

<p>If it appears to not work on a particular website then that is likely a bug on the platform and it is worth reporting to the platform.</p>

<blockquote>
  <p>Some (possibly in/correct) answers <a href="https://www.quora.com/How-do-you-checkmate-with-a-king-and-a-bishop-how-does-the-strategy-works" rel="noreferrer">here</a> state that the rules of
  chess deem such a situation to not have sufficient mating material. I
  am not sure how reliable they are.</p>
</blockquote>

<p>No, what you say is not correct. The question on the Quora website is not the same. It is asking about <em>forced</em> checkmate. If your flag falls then the opponent does not need enough material to be able to <em>force</em> checkmate. He only needs enough material to checkmate you with you making the worst possible moves. If that is possible then you lose on time. Only if there is no possible sequence of moves leading to checkmate do you get a draw. </p>
 19877: <p>First, Carlsen, despite having only the Bishop, WON that game. So it is not about mating material, but about ANY possible mating position, and there was one here.</p>

<p>The rule at hand is this:</p>

<blockquote>
  <p>Paragraph 6.9 of the FIDE Laws of Chess state:</p>
  
  <p>The game is drawn, if the position is such that the opponent cannot
  checkmate the player’s king by any possible series of legal moves.</p>
</blockquote>

<p>There were positions that white could be mated, even though it required total cooperation, and there is no way that Firouzja would have allowed it. That was irrelevant, so it was a loss.</p>

<p>Also see this related <a href="https://chess.stackexchange.com/questions/27756/what-exactly-happened-in-the-open-world-blitz-championship-in-game-carlsen-alire/27758#27758">question</a>.</p>

<p>Here are the USCF rules.</p>

<p>14D. Insufficient material to continue.</p>

<p>The game is drawn when one of the following endings exists as of the most recently determined legal move, in which the possibility of a win is excluded for either side. </p>

<p>14D1. King vs. king.</p>

<p>14D2. King vs. king with bishop or knight.</p>

<p>14D3. King and bishop vs. king and bishop, with both bishops on diagonals of the same color. </p>

<p>14D4. No legal moves leading to checkmate by opponent. There are no legal moves that could lead to the player being checkmated by the opponent</p>

<p>So, even these rules are quite specific as to the material for an automatic draw.</p>
