Seth J. Mazor
It's actually a bit of both. The rules regarding end game are not well written.
Yes, there are more bribe chips in each round and yes you can trigger an early end, but the normal end still trumps the "last turns".
...in these cases, everybody, including the player who caused the early end of the game, gets one last turn.
If during this last round the game ends normally, it ends at once, even if not everyone has received his last turn.
That "normal end" comes about if someone takes the last bribe chip and triggers pay out.