Despite what the movies would have you believe, even in the extremely rare cases when an entire section of fuselage rips off an airliner at over 30,000 feet, everyone inside doesn't get sucked out a big hole. In the even more rare cases that someone does get "sucked out", it is always someone like a flight attendant or other unlucky soul who happened to be standing up, unbuckled, right next to the opening.
This "sucking" only continues until the pressure inside the fuselage (which is much higher, since the people inside tend to consider enough oxygen to breathe as included in the price of the ticket) equalizes with the pressure outside. If the hole is large enough for a person to go through, this equalization will take place in a matter of seconds. After that, all that loud noise and wind will be from air outside the aircraft coming in just like the wind does when you roll down the windows in your car. (That's assuming your car has 10-foot windows and is going 500 MPH.) Take comfort in the knowledge that in almost all cases of pressurization problems, the loss of cabin pressure is slow and is caused by either a stuck valve in the system itself or a gap that opened up somewhere in between the pressurized and unpressurized parts of the aircraft that is small enough that even a @#$% snake on a @#$% plane couldn't squeeze through.
The reason I put "sucking" in scare quotes above is because the air inside the plane isn't being "sucked" out. In reality, what is happening is that the higher-pressure air inside is flowing violently outside to where the pressure is much lower. It's exactly the same principle as what happens when you blow up a balloon then instead of tying the end, you let the air come out, making a noise that sounds like a session of Congress. If you let the air come out long enough, eventually all of it will be gone and it will stop flowing.
Now that I've spent three paragraphs explaining what happens in airliners, I'll get to the Piper Malibu referred to in the news story by saying that it has almost nothing in common with an airliner. Even if the entire top of the aircraft fell off, its service ceiling is about 10,000 feet lower than an airliner's typical cruising altitude so the difference in pressure between inside and outside is much lower, the cabin is much, much smaller so there's less air to "suck", and it goes less than half as fast. In addition, it has a "Door Unlatched" annunciator light in the cockpit, so the pilot wouldn't be able to take off with the door ajar without knowing it. (I mention that because the pilot reported that he had an open door.)
Will an airplane fly with a door open? You bet it will. In fact, I've had doors unlatch on me in flight dozens of times; it's just one of those things that happens occasionally. Most of them are designed—just like the doors on your car—so that if they do accidentally come unlatched the air flowing past the fuselage will keep them pressed mostly closed. The plane itself doesn't care, and it will keep on flying happily along with almost no noticeable difference other than a higher-than-normal level of cockpit noise and a nice cooling breeze along the forehead (in Cirrus and Piper aircraft).
In fact, this is such a common occurrence in Piper Seminoles that when I took my CFII checkride, I semi-jokingly included in my pre-takeoff briefing to the examiner: "Once the door pops open on the takeoff roll, I will bring both throttles to idle, contact tower to let them know we are aborting the takeoff, exit at Taxiway E, secure the door once we are clear of the runway, and ask to taxi back for takeoff again." Can you guess what happened one minute later? (To be fair, this doesn't happen all the time. I only said it because I knew that a quirk of the particular aircraft I was in that day was that its door latch was like Jay Leno: old, worn out, and desperately in need of replacement.)
When a student is getting close to solo in a Cirrus, I will intentionally pop the door open in the traffic pattern to see how they react. If they continue around the pattern, land, and then address the door, I know they are doing just fine. The first priority of an aviator is always, always, always, no matter what happens, always fly the plane.
An open door isn't even an emergency, but most manufacturers have a procedure to handle it just in case. This usually boils down to a simple matter of slowing to about 80 knots, opening a window, and closing the door again. It is considered such a minor matter than some manufacturers actually put the "Door open in flight" checklist in the "Normal Procedures" section of the manual. Piper is not one of those, but they do have a checklist for it. The first few lines of it are simply:
If both upper and side latches are open, the door will trail slightly open and airspeeds will be reduced slightly.
To close the door in flight.
Slow airplane to 82 KIAS.
Cabin vents ... close
Storm window ... open
Many aircraft will fly perfectly well even if a door is removed. Skydivers do that all the time, and I flew a Cessna 182 with the right door taken off when I dropped the famous Golden Knight turned motivational speaker Dana Bowman on one of his jumps in 2012. I could hardly tell a difference, other than with the weight of the right seat and door gone, the plane actually performed a bit better.
I'm not going to speculate on what actually happened in that Piper Malibu. That's for the investigators to figure out. All I'm here to do is to tell you what won't happen in an airplane: you won't fall out of one if you fly. So go out and enjoy it!