Reading the article:

Certainly, humans are endowed with some sort of predisposition toward language learning. The substantive issue is whether a full description of that predisposition incorporates anything that entails specific contingent facts about natural languages.

So this makes it sound like the only thing the authors are rejecting is the idea of a system with certain rigid assumptions built in - as opposed to, say, a more or less Bayesian system that has a prior which favors certain assumptions without making those assumptions indefeasible. Am I reading that right?