I think we are confusing ourselves because multiple plays have been introduced in this thread, and we are responding (correctly) to a play, but then someone else thinks we're responding (incorrectly) to another play they were reading.
Rule 3, Section 4, Art 3, a-j give us "major" clock stoppers.
Kid fair catches the ball and we have illegal formation and K replays 4th down? Clock on the snap (3-4-3j)
Kid does not fair catch and runs out of bounds and we have illegal formation and K replays 4th down? Clock on the snap (3-4-3a)
Kid does not fair catch and is tackled inbounds and we have illegal formation and K replays 4th down? Clock starts on the RFP