I let one of my players borrow my game, so I don't have the rules handy. Tonight I enforced the secrecy rules as much as possible with my group. Particularly, I made sure that a) a choice, without discussion, on a Crisis Card had to be made before showing the card and b) when given a choice between two cards (i.e. crisis/destination) the choice had to be made without discussion and you couldn't say what the other one was. NB: we were mostly newbies who didn't know what the cards were so we fudged secrecy some.
That got me thinking. Certainly, it cannot be that you don't show the crisis/destination card you have (unless a skill check), that you simply say what it was, can it? For example, when given a choice between -1 morale or -1 pop (if such a card exists) you simply say "alright, guys, we lose a pop" or "we lose a morale" without actually showing the card. Likewise, the Admiral says "well, we lose 2 fuel and jump 2 spaces." I can see a lot of cheating going on, despite 'trust-worthy' players.