No.

It is based on the premise that if the proprietary licenses are valid, then also the open source licenses are valid.

So what is held as true is only the implication stated above and not the truth value of the claims that either kind of licenses are valid.

If the proprietary licenses are not valid, then it does not matter that also the open source licenses are not valid.

The open source licenses are intended as defenses against the people who would otherwise attempt to claim ownership of that code and apply a proprietary license to the code, i.e. exactly what now Anthropic and the like have done, together with their corporate customers.

Of course, if it is accepted that the code generated by an AI coding assistant is not copyrightable, then using it would not really be a violation of the original open source licenses. The problem is that even if this principle is the one accepted legally, at least for now, both Anthropic and their corporate customers appear to assume that they own the copyright for this code that should have been either non-copyrightable or governed by the original licenses of the code used for training.