Part of that statement is correct, part of it is misleading.

> AMP required allowing any AMP CDN to cache your pages.

Sort of correct: this is true if and only if you wanted the rank boost for Google search. If you just wanted to serve AMP and have snappy page, not entirely correct.

> other scripts on your site might be incapable of running on your AMP site

Correct, because that's the entire point of AMP. It is a straightjacket intended to make it technically impossible for your "other scripts" to run, because actual users hate your "other scripts" and they make users' phones overheat etc.