6-5-3: Only the receiver who gives a valid signal is afforded protection. If, after a receiver signals, the catch is made by a teammate, it is not a fair catch but the ball becomes dead.
You can only specify where, between the hash marks, the ball will next be put in play after a fair catch but not other received kicks. (4-3-6)
To answer the question directly, no, you would not grant the request. The ball will be next put in play at the spot where it became dead.