"BSD license but secretly I'm not going to let you relicense" means that you have not in fact contributed under the BSD license in the first place, but your secret license.
I understand what you're saying, but even if you do release BSD software along with code under a different license, you are still bound by the (very minimal) requirements of the BSD license.
I understand what you're saying, but even if you do release BSD software along with code under a different license, you are still bound by the (very minimal) requirements of the BSD license.