A few disjointed, semi-connected thoughts:
1. Suden is correct about the rule here. You have the right to verify the legality of opponent's gameplay. That includes verifying that opponent included all relevant targets in a selection.
2. The Rulebook is clear and unambiguous about it, winterflames already quoted it, and that's as official as it gets.
3. The principal that you can verify the legality of opponent's gameplay is fundamental to the game. There are very, very rare exceptions where you don't get to verify legality immediately (namely hidden agenda plays and download-and-seed actions), but you do eventually get to verify them (after the game) -- and the penalty for violating those rules is automatic forfeit, even after you've already won the game, even if the rules violation was accidental and made no difference to the outcome. "Inability to verify" is a reason several card designs have been shot down. (Have you noticed that cards always "seed or play" or "play" but never just "seed"? This is why.)
4. This is considered so important because the game has no recovery mechanism if a rule is violated but nobody notices until later on. Suppose you face Female's Love Interest and you accidentally forget to include a certain female in the selection. Then while facing the next dilemma, that same female helps overcome Barclay's Protomorphosis Disease, saving the entire Away Team. At the end of the attempt, after facing two more dilemmas, you or your opponent suddenly notices the error made back during the Love Interest encounter. What can be done? According to the rules, nothing! You can't truly undo the mistake, so you just keep playing. Because innocent rules mistakes by one player can have enormous negative consequences for the other player, the rules give both players the power and the responsibility to ensure that innocent rules mistakes don't happen. That means card verification.
5. As far as I know, this has always been the rule. It is consistent with the old Glossary and with Decipher's other thinking about card verification, although the new Rulebook was the first document to spell it out in vivid clarity like this.
6. For some reason I don't entirely understand, while it has seemingly always been the rule, many veteran players are unaware of it or confused about it. (Veteran players are especially resistant to the idea that you get to see cards that are not included in a selection.) I suspect it's because some combination of (a) Decipher enforced it inconsistently or unclearly, and (b) the old Glossary text did not really spell out all the consequences, choosing to depend on a nonexclusive "includes" clause. Geraldkw is clearly correct that, whatever the cause, different playgroups evolved very different customs around this.
7. In any event, it is sometimes necessary in games to point competitors to the rule. It is understandable that they will be surprised that there's a 20-year-old rule they didn't know about. It is courteous for them to gracefully acknowledge their error.
8. At the same time, it is courteous for you as a player to not always insist on the letter of the law if you have no reason to believe it is necessary to preserve the integrity of the game.
(Among other things, verification of all actions can become very time consuming and turn the game into a grind. If I see 15 dudes on my opponent's ship, I am not going to ask him to prove staffing every single time he moves it, even though I have the right to do so. I only sometimes "spot check" dilemma targets. Although I might check every time at Worlds, there's no reason to be that assertive in a casual.)
9. It is certainly both possible and legal to use this rule in order to scout opponent's cards, but that is not the intent of the rule, and the rule actually goes to some lengths to prevent it (using the "you only have to show the relevant portions" rule). Because it is legal but counter to the intent of the rule, some players may see it as a dick move, and they may even be right.
(What counts as a "dick move" is above my paygrade; I can only tell you if it's legal. This is not the first time we've had a dispute about whether exploiting a perverse but legal loophole is dickish or not.)
10. It does kinda suck that online play makes it impossible to use the rule that you only have to reveal the "relevant parts" of cards when doing verification. You end up having to reveal all your cards upon request. That makes the scouting effect much stronger in online play, which is bad.
11. Online play specifically has some acknowledged deviations from the official rules. For example, in online play, you seed cards top-to-bottom (instead of the legal bottom-to-top). These tend to evolve by community custom, until, eventually, Organized Play officially ratifies them.
12. So, if someone has some clever idea for only revealing "relevant" parts of cards to opponent in online play, by all means, have at it, see if it catches on, and eventually I'm sure it will become an official part of online play. But any solution will have to respect the rule that you always get to verify the legality of your opponent's gameplay.
I think that answers all the questions that I was asked (plus several I wasn't).
"We pledge our loyalty to the Glossary from now until death."
"Then receive this reward from the Glossary. May it keep you strong."