False. If I take a BSD/MIT library and fork it, I don't need to contribute the changes back.
The MPL(v2) forces forks to be open source, but any files added to the project can remain closed source allowing it to be used as a library for closed source applications.
Copyleft is about pay-it-forward not reciprocity. There's zero reciprocity in copyleft besides the incidental fact that updates paid-forward to others might be discovered and accessed by the original person who gave you the software (or that you could share the updates back in reciprocity, but that's not part of the license, it's just something you might do).
The MPL(v2) forces forks to be open source, but any files added to the project can remain closed source allowing it to be used as a library for closed source applications.