This is true, but there's also a murkier middle option. I used to work for a company that made a lot of money from its software patents but I was in a division that worked heavily in open-source code. We were forbidden to contribute to the high-value patented code because it was impossible to know whether we were "tainted" by knowledge of GPL code.
Same here. I worked at a NAS storage (NFS) vendor and this was a common practice. Could not look at server implementation in Linux kernel and open source NFS client team could not look at proprietary server code.
No you are not, guaranteed (I think, not a lawyer).
At least from a copyright point of few.
TL;DR: Having right, and having a easy defense in a law suite are not the same.
BUT separating it makes defending any law-suite against them because of copyright and patent law much easier. It also prevents any employee from "copying GPL(or similar) code verbatim from memory"(1) (or even worse the clipboard) sure the employee "should" not do it but by separating them you can be more sure they don't, and in turn makes it easier to defent in curt especially wrt. "independent creation".
There is also patent law shenanigans.
(1): Which is what GitHub Copilot is sometimes doing IMHO.