This is the way I see it:
If we go by these 2 official rules about the trash:
The Trash pile is on the Trash mat, face up; players may look through the Trash at any time.
The order of the Trash pile does not matter; players can reorder it.
Then we conclude that the trash mat can be shuffled and messed with at any time without interfering with any other game mechanics. The trash is basically just a display of cards that are in it; said cards aren't stored in some kind of precise array. They are only stored in a pile not because of their trashed order, but because it's more convenient to have them that way. But the trash could very well be cards put next to each other*. The fact that the trash can be moved around at "any time" means precisely that. A player could pick up the trash and shuffle it midway through a played card being currently resolved; in fact, the turn doesn't even have to be yours for you to do that. Again, this is because you're doing that at "any time".
Going by that logic, then before the Noble Brigand finishes being resolved, a player could look through a trash pile with, say, 10 cards in it, including a Gold that was just trashed by that Noble Brigand. They could then shuffle that pile behind their back and put it back on the mat. The active player who played the Noble Brigand would then finish what the card says by gaining the trashed Gold from that pile. Since the deck was shuffled, oops, nobody knows where the exact trashed Gold is anymore! Especially if there are more than 1 Gold in that trash.
Yet as mentioned earlier, the 2 rules above states that checking and reordering the trash pile has no effect whatsoever on the Gameplay. It's a passive rule. Therefore, it should not affect the gameplay in this situation either; so it won't. If that rule was not enforced, then Noble Brigand (and cards like Thief), no matter what situation, could always break since any player at any time can mess up the trash pile. Any Noble Brigand played would be met with another player swiftly putting the Gold that was just trashed under the trash pile (because, again, the may do so at "any time") before whoever played the Brigand gets to pick it back up.
Thus by that logic and to avoid fundamental contradictions, the Noble Brigand can pick up any Gold in trash since it does not have to remember which one they put there in the first place. Whether it's "that card" or not is irrelevant, because if "that card" had to be it, then Noble Brigand would never work anyway.
Here's another situation to highlight the absurdity of Noble Brigand being unable to pick up a Gold it just trashed because it doesn't remember which one it is.
3-player game. You play a Noble Brigand. The player to your left trashes a Silver. The player to your right trashes a Gold. Now you do the bottom clause of Noble Brigand: gaining the trashed Treasures. You try to pick up the trashed Silver. Oops! It isn't on top of the trash pile (the Gold is). You've lost track of the trashed Silver! Now you can't gain it.
Or, you know, just move the Gold out and pick up the Silver. Or gain the Gold first. Whatever. In the end, it's all the same.
*The only subtlty in storing the trashed cards is to have them face up, for the sake of Necromancer. But that's it.