Can they do this?

[GarthB]

Originally Posted by CO ump

Don't remember it ever happening, but Yes

Wow. It happens a lot here. Fielder will take advantage of the time out and throw the ball around.

If we go back to the OP, before posters started assuming a relief pitcher was involved, I don't see a drastic difference between that scenario and the one I suggested.

I believe the FED rule is intended to preempt incoming relief pitchers from getting extra throws, not to prevent fielders from "staying loose."