Theoretically, managers can't block you from having 20% time, and there's no official permission process you need to go through to take it, but if your manager says, "I'll fuck you over in Perf if you do a 20% project", then you don't have 20%-time.

What I'm told is that, before 2007 or so, Google actively worked to avoid manager-as-SPOF, and that this is what made Google great. But then they hired a bunch of executives from mainstream large companies and didn't tell them to wipe their fucking feet off before coming inside.