> I think it would be extremely surprising for Universal Grammar to be proven false.All you need to make it unsurprising you need to find an alternative hypothesis, that can explain observed facts.
How about this one. Humans got the ability to abstract deeper than others. While some animals could deal with concepts closely associated with real phenomena, and therefore they can use words to name things or maybe even actions, they cannot go further and use abstractions over abstractions. As the result they cannot deal with a recursive grammar.
Or another hypothesis. Humans got an ability to reflect on themselves, so they came to concepts like "motive (of action)", it made it possible for them to talk about actions, inventing words-categories, that categorize actions by supposed motive of action. But it is not just that, people started to feel that simple words do not describe the reality good enough, because a) actions have more than one motive, b) they started to see actions everywhere (the stone is lying flat? it is the action of the stone, that strictly speaking cannot act.). All this led them to invent complex grammars to describe the world where they live. Animals from other hand can't get it, because their world is much simplier. They don't see the stone "lying": it is a stone, it cannot do anything.
These hypotheses don't seem explaining everything, but I have just invented them. I didn't really tried to explain everything. But thinking about it, I'm in favor of the second one: all people are schizophrenics if you compare them with animals. They believe in things that are not exist, they see inanimate objects as animate, they are talking with themselves (inner dialog). It just happens that the particular kind of schizophrenia most people are struggling with is a condition that allows them to not tear apart all the connections with the Reality. It is more like borderline schizophrenia.