The problem with the Chomsky nonsense about how the syntax of a language can't be learned from input (so much, so fast, with such bad data!), so it must be innate, is that they are not proving that the input is insufficient. They're just claiming it. They just say that they don't see how we could learn so much from so little, so it can't be done, so it isn't learned, it's inborn.
That's just the creationist argument: I can't see any way that something as complex as a human could emerge randomly, so it must have been assembled deliberately by a super-human creator. There's no other way.
Well, no. The thing you're missing here is that there might be algorithms that can do more than you realize.
If the Chomskians proved that the information to be learned simply didn't exist in the input--not that they didn't see it, but using information theoretic methods proved that it could not be there, then the learning algorithm wouldn't matter. It would not be possible for any algorithm.
But unless linguists prove the needed info isn't there (which is probably not possible using our limited knowledge of information theory), the ockham's razor hypothesis for how kids end up speaking the exact dialect they're surrounded with is that they possess algorithms capable of extracting the information from their surroundings.
Declaring such learning impossible because it doesn't look possible is like declaring human evolution impossible for the same reason. We're just beginning to discover that there are spectacularly powerful algorithms capable of doing things we never imagined.