Assuming a tournament with a top-16 cut. The top 8 should have better ratings gains from the playoff games than the losers of the first round. Likewise, the top 4 should have better gains than the losers of round 2. The finalists have better gains than the semifinal losers. And the winner has better gains than the second place player.
If the 3/4 game is played for points, then not only does the 4th place player get bumped down to a similar ratings bonus as 5-8, the 3rd place player gets bumped up to the same ratings bonus as the 2nd place player who quite probably beat them in the previous round.
A prize being on the line does not mean it has to be a points match. An official judge officiating it doesn't mean it has to be a points match. And there are plenty of games which are sanctioned by POP and officiated by official judges which are not played for points (Prereleases, fun format, unlimited format, non-premier tournaments, etc.)
I know this was a rambling post, but all my points converge on the central one that this game between third and fourth place doesn't have to be, and shouldn't be, a game with points on the line. (by "doesn't have to be" I mean that logically speaking, not according to the official tournament guidelines, which I admit I haven't read closely for premier tournaments.)