A character of Alignment X believes Y. The problem comes is that the meaning of Y is often somewhat up for grabs. But, when the DM decides that Y=one thing and the player decides that Y=something else, then you have a recipe for trouble.
Yes. And a GM who doesn't lay down some of what he thinks on the matter, and maintains a dialogue open on the matter will usually dispel such problems.
If, at it's root, the problem is that players and GMs fail to communicate, then the problem is not in the rules, but in the players and GM.*
After all, the DM is encouraged to make sure that players are playing their characters. All the way back in 1e, the training rules talk about players not playing their characters being forced to spend extra time training. Granted it wasn't directly linked to alignment, but, it's not too much of a stretch to connect the dots.
Never minding classes where alignment actually has direct impact as well - the paladin being probably the biggest issue here. But other classes often have alignment elements built into them as well.
Don't you see how those two, when connected, say exactly the opposite of, "Your character wouldn't do that!"? The rules *explicitly* talk about paladins falling. Therefore, the characters *must* be able to take such actions, or falling wouldn't be an option. The rules thus specifically tell you that your character very well CAN misbehave - just that there are consequences.
In any event, my personal experience is that, "Your character wouldn't do that!" statements don't depend upon misunderstanding of the rules. Every time I see them, they are instead desperate attempts by a player or GM to keep another player from doing some particular unexpected thing that they personally don't want to happen. I always seen it invoked as a defense mechanism against some perceived (sometimes rightly perceived) wrong against their persons or vision of how things should unfold, a rationalization meant to corral someone.
Most often, it was basically to the effect of, "I'm playing the Chaotic. I get to do what I want and say, 'I'm only playing my character!'. You're playing the Lawful. I'm supposed to be able to take advantage of you, but you, being Lawful, have to follow rules and can't go cutting me down in cold blood for it! Nyah, nyah!"
I'm sure that somewhere, it happens else-wise, as real misunderstanding. But I've never seen it happen that way. Thus my position on entitlement and role-play expectations, not on rules.
And, let's be honest, it's not the easiest thing to discuss morality in any situation. People can get right testy very quickly when you start talking about morality.
True.... but see below.
Heck, all you have to do is watch the alignment discussions on En World whenever someone claims that His Favorite Character has to be a particular alignment.
I don't know about you, but my table works rather like EN World - if you cannot discuss the game as mature, controlled adults, I'm not really interested in having you around.
*I don't know the attribution, but there's a sort of rule for fiction - if your work's major plot would completely unravel if the main characters did the stunningly intelligent thing and sat down and talked like mature adults, it isn't a very good plot. Similar thing here. The rules will never guard you against people being that dim, so don't expect them to try.