I know about Montana's many comebacks. I've poured over game summaries from those years and am amazed at how many comebacks he had that aren't talked about.
I also know about the cold weather (its just about all they talked about during the game cast) and Montana's sickness.
I just think that Montana was only a very small part of this comeback, and in the retelling really shouldn't be singled out at all. The chicken soup part of the story really deserves no mention. Houston may not have had a first down in their last 7 drives. Special teams blocked two punts and got the benefit of bad snaps on two others. Houston also made a Kelly-like decision to go for it on 4th down in his own territory with a minute left. And Montana had a lot of really awful throws and three turnovers after he came back.
If Montana hadn't had all those other comebacks and gone on to a great career, we would be saying they came back despite having Joe Montana at QB. Instead, the comeback gets retold as part of that Montana magic.