Actually, you are not allowed to look at the cards in your main deck mid-game, so I'm not sure this is a good analogy...
Some abilities put cards into play facedown. A facedown card has no inherent attributes other than "facedown card," but it may be granted attributes by the card ability that put it into play.
- A player may look at the identity of any facedown card that is in play and under his or her control.
- Agenda cards are not considered "in play." Their text affects the game state from the out of play area while they are active beside a player's faction card.
The RRG only refers to facedown cards in play - in particular, stating that you can look at facedown cards that are in play under your control, and in general, referring to cards being put into play facedown.
The wording seems to imply that facedown cards can only exist in play - or at least that the designers thought of them that way when writing that RRG entry.
However, in other card games there are card effects that instruct a player to "remove cards from the game facedown", and it is not unreasonable to assume that we might get facedown out-of-play cards in AGOT at some point.
The agenda card itself is not considered to be in play, but that doesn't quite mean that cards under the agenda are also not in play.
I think we can assume that facedown cards under the agenda are in fact considered to be in play, and so their controller can look at them at will. Incidentally, that would mean that we can use Unbridled Generosity to place gold on these facedown cards
Actually, cards in the plot deck and in the main deck are in fact facedown cards, and they are not in play. You can look at facedown cards in your plot deck, but you cannot look at facedown cards in your main deck. So I don't see a definite answer...