I think one good reasoning for BoM's interaction with both +1 Action tokens is as follows.
When you play BoM, first you check whether the BoM pile has a +1 Action token. If it does, the BoM card essentially becomes a card that reads:
+1 Action
<Text of BoM card>.
So you get any +1 Action before you even begin to read what the BoM card's text says.
Then you read what BoM says, and it says to play it as if it were a certain card from the supply costing less than it. Okay, you pick that card. If that card happens to have the +1 Action token on it instead, then you would get the +1 Action before beginning to read the text on that card.
Therefore, BoM can give you the +1 Action from either pile.
--
With Throne Room, it may be that when the +1 Action token is on BoM you only get it for the first TR play, as once BoM becomes the second card ("Until it leaves play"), it can't get the +1 Action for the second play. That'll need a FAQ or ruling clarification.