The more I read and the more I think about it, I really don't like the idea of secret rolls for EotE. I think it's a relatively mature system, in that GMs need to trust their players to play the story, rather than the rules. I know not all groups are like that, but I think addressing it beforehand with something like this: "There are times when you as a player are going to know things that your character will not. Let's try to play out what would happen for the characters, rather than what would happen for the players." It's not worded right, I know, but I'd hope that it would work out, that the gist would be there.
It also allows trust in the other direction, if you aren't hiding any rolls from your players either. All adversary rolls or environment rolls should be done in the open, and just go with the flow, working it out as you go along.
After all, this is supposed to be a story-driven RPG, where the GM and other players create a story together. Actually, as a slight aside, I really enjoyed the comment on (I think) the Order 66 podcast, where it was said that the dice rolling in this game isn't the end point of a character's action, but the middle point. I found that helpful.
"There is no point to owning a copy of the rules if you aren't committed to actually reading them."