The lie is saying "Cardinal Müller has persistently come out in favour of the four Cardinals until today..." when he has consistently supported the Pope. He believes that the teaching you describe "that couples living in adulterous relationships should not receive Holy Communion" is fully consistent with AL. You cannot assume that he is supporting the position of the 4 cardinals just because he affirms that position. He is pretty explicit about being on the Pope's side when he affirms that teaching.

This is actually the point Müller was addressing when he said people need to look at the issue more objectively. Affirming "that couples living in adulterous relationships should not receive Holy Communion" does NOT mean he is supporting the cardinals, but some people assert that it does mean that because they are inclined to identify that position with the cardinals instead of with the Pope.