IANAL, but I think that if they were to assert copyright over your code, the license you chose would be irrelevant (since the code was never yours to license in the first place).
I should have clarified (and it's too late to edit) that this refers to code I wrote and licensed before the applicable employment. It was already made public under a BSD/MIT license, so everyone (including me) is allowed to use and fork that version, even the ownership later changes and the new owner licenses theirs differently.
Maybe. If you’re a senior engineer, I could also imagine arguing that I had authority to license it under BSD or whatever as an agent of my employer. The argument would probably be much stronger if you got sign off from your boss though. And legal if your company is big enough. (Though IANAL)
