Rule 6 Section 12 covers face-offs.  As a short answer, the "official
shall order the individual(s) taking the face-off replaced for that face-off by
any teammate(s) on the ice".  So much for the authority to make the change.
Maybe your question was more about "sometimes they fake like they are going
to drop the puck" and any such "faking" would draw the ire of several
people so no official should be doing that.  Someplace I have read
instructions for the correct procedure for an official to use, but on a
quick perusal I couldn't find it in the rule book so must have heard
it elsewhere.