You're right. But it is a parody.That isn't satire.
I don't know if I'd call it a satire. A satire involves actual criticism of something. Great examples of satire are 1984, Animal Farm, and Brave New World. That's satire.The word parody gets thrown around way too often in my opinion.
Airplane is a satire of all the disaster movies around the time.
Airplane, from what I could tell, wasn't trying to make any real point about the disaster film genre, it was just using the framework as an opportunity for jokes. That's a parody, but not satire.