6721-
Do you understand what an appointee is? You can be appointed by someone- and then have autonomy. If you are a very bad performer- and depending on the unique circumstances of the board you are appointed to- then you may not be renewed or you could be asked to resign.(Heckova job, Brownie!)
There are multiple examples of other Fed appointees having autonomy once appointed- I'll leave that for you to research on your own.
And, if you think about it for 10 seconds- do you really think it is Obama himself, and thus another reason for you to tell us why we should hate him every single day here, that told all 5 members how to act on this specific issue? I really don't want your answer on this one.