Humans generally can't gain native-level fluency in a language unless they are exposed to it as young children.
The only aspect of language with a critical period is accent. Adults commonly achieve fluency. In fact, adults learn a second language faster than children.
As far as I know, the degree to which second-language speakers can acquire native-like competence in domains other than phonetics is somewhat debated. Anecdotally, it's a rare person who manages to never make a syntactic error that a native speaker wouldn't make, and there are some aspects of language (I'm told that subjunctive in French and aspect in Slavic languages may be examples) that may be impossible to fully acquire for non-native speakers.
So I wouldn't accept this theoretical assertion without further evidence; and for all practical purposes, the claim that you have to learn a language as a child in order to become perfect (in the sense of native-like) with it is true.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.