The idea that the ability to grok recursive structures is due to some part of human physiology that is unique to humans is pretty much taken as a given in Chomskyan linguistics, almost to the point of religious belief -- it's Chomsky's organ kundabuffer. Ask a Chomskyist to identify this organ or structure and they will handwave: "Well, we don't know exactly what or where it is but we know it's there, humans have it and animals don't so nyeh. We've prebunked any promising animal language study you can produce."