The researchers are identfiying that languages that lost V2 may have underwent specific other syntactic changes in the same period. Since these changes co-occurred in multiple languages at different times, they suggest it's likely there is an underlying structure linking them (...which they conveniently have an explanation for within their particular brand of universalism).

Of course just because language has deeper structures doesn't mean the structures are actually universal. I happen to like a lot of the syntactic mechanisms suggested by minimalists (the work on things like adjective order and clause relations is fascinating) but I don't necessarily believe it's compelling that any of it is an inherent feature in the brain...

EDIT: Here are some presentations by the authors, though I must admit I don't have the time to look though at the moment. http://www.hf.uio.no/ilos/english/research/projects/traces-o...

That describes so much of the history of Chomsky's theories...