The message speaks directly to the controller of Ultimate Offering and no one else. Woo0 quotes the message where they specifically say only the controller can use it.
The confusion over this card comes from the old text which used to say "a player" may pay 500 Life Points to Normal Summon a monster. Which was not the way Konami wanted it to work. In fact, the card was grossly inaccurate as the effect text didn't work at all like it was supposed to. Here's the old text:
At the cost of 500 Life Points per monster, a player is allowed an extra Normal Summon or Set.
See how vague that wording is? It said nothing about when it could be used and ambiguously left it open for both players to use. They posted on the Judges List several times how they wanted it to be played. In fact, it's one of the few instances on the list where you here an answer that equates to "Because Konami Said So" Here's the current text:
By paying 500 Life Points, Normal Summon or Set 1 extra monster. You can only activate this effect during your Main Phase or your opponent's Battle Phase.
As you can see, they removed "a player". And no card can be used by both players unless the effect text specifically says so.
