So far, I've been able to escape Falco's chaingrab with Samus, even at Falco's first attempt. That is to say, he'll grab me and throw me down, but the moment I hit the ground, I'm in the air, jumping and DI'ing out of the way. Thus, Falco's chaingrab is rendered useless. This doesn't work for most characters, though. I was unable to do this with Pit and Fox, though it seems that at the third attempt, Fox can get free.
Samus, Kirby, Jigglypuff, Peach.
Those are the characters that can escape for sure. The rest... it's questionable.
And you don't need to double-jump airdodge, you can just do their Nairs, Fairs... anything, really.
Anyway, Ref, I think you're in error. Just because it's called a "chaingrab" doesn't mean that you cannot escape it. There's a difference between "chaingrab" and "infinite chaingrab." You should keep in mind that in reality, chains are limited, and thus come to an end.
They are called chain grabs because you can't escape them without having your opponent mess up or having the chain grab finish.
Actually, I think he got it dead on.
Let me clear this up. Falco's chaingrab not being 100% on those 4 characters doesn't mean chaingrabs are escapable. It means Falco doesn't have a true chaingrab on those 4 characters. A chaingrab is, literally, a chain of grabs that you CANNOT escape when it's performed correctly, until you reach the end of the stage, certain percent, etc.
An Infinite Chaingrab is something that you cant escape, ever, until either your opponent messes up, or decides to let you out. Or a hazard hits you, or something just as "fun".
Suffice to say, yes, this is the most common method for escaping a chaingrab when your opponent messes up, right next to spotdodging.