the simplest answer is to say that the "Cosmic deck" ... is "the deck," and the Rewards deck is the Rewards deck. I'd say Remora and Wild Mind do not interact with the Rewards deck.
I think you're right. Today I researched every FFG power and flare that uses either the word "deck" or the word "draw" to see if that would cause any questions or other problems. I don't think it does. The overwhelming majority of uses of the word "deck" are in the phrase "draw card(s) from the deck", which in context almost always means pretty obviously only the cosmic deck. Here are a few noteworthy examples, and they all work just fine with your interpretation:
Wild Ethic — "When you draw any new card(s) from the deck ... you may feel guilty and give away some or all" — so Wild Ethic just can't feel guilty about reward cards; that's fine.
Wild Genius —"force any number of players ... to draw a card" — from the deck is implied here, and clearly nobody would argue that anyone gets to draw a reward card.
Wild Mind — "each time that player must draw a card from the deck, you may draw it instead, look at it, and then give it to him or her" — so we're saying this is only triggered by, and only affects, cosmic deck draws. Works fine.
Remora — "Whenever another player draws one or more cards from the deck, you may use this power to draw one card from the deck" — again, only triggered by, and only affects, cosmic deck draws. Again, works fine.
I like your interpretation: "The" deck is THE deck; there's only one.
Now, having said that, I think there are two other cases that do not fall under this interpretation:
Gambler — "If your opponent does not challenge your claim ... place your encounter card facedown on the bottom of the deck" — this needs errata anyway to say something like "the bottom of the appropriate deck". Clearly we can't be stuffing reward cards under the cosmic deck.
Super Mercenary — "When drawing cards for rewards, you may discard any or all of them" — I say this effect, unlike the other examples above, does work with the reward deck. It doesn't say "the deck" and it specifically targets the drawing of rewards (which of course can come from either deck).