I work for a HUGE information company ( until December by my own choice) and they actually do this shit. And then threaten you if you question their process.
You work for us but you are entrepreneurs! Grow your personal brand but tie it directly to us! You have a Facebook account? You must mention us in anything you do that involves your work!
Making you reapply for your current position? Yes, we are, but you can't solicit work on your PERSONAL website.
FUCK THAT.