I just have a simple take on it... "see" for purposes of missile fire or spell casting means the same thing as "unobstructed line of sight." So no distinctions between "visible" or "sight" either, it's all just the same thing.
Otherwise I'm saying you can be in a single square wide corridor and there's a row of orcs ahead of you and you can shoot the last one in line with your crossbow, bypassing all the other orcs ahead of him. I don't allow that. The first one in line blocks the rest of them, even though you know they are there, you can't hit them. Same with magic. So if the heroes are all lined up and the Wizard is bringing up the rear and the dwarf is next to him and then the elf and finally the barbarian is the further away, sorry, the Wizard can only cast a spell on himself or the dwarf... and the elf can only cast on himself, the barbarian, or the dwarf but not the wizard.
While I am choosing to interpret"see" for the purposes of searching to just mean are they on the board in the same room/corridor with you.
Avalon Hill's take on seeing for the purposes of searching is very old school and literal. If you're in the room with a monster, even if he's in a corner surrounded by friendly characters and there's a bookcase between you and him (and under a Sleep spell), it doesn't matter... you can't search for anything because the enemy is "present" in the room.
If if there's an open doorway and you could trace a line out that doorway and there's a monster in the next room or corridor from where you are, THAT stops the search (I think that's silly, but that's what is there and they don't want to change it). Now swap that door for a secret door, even if it's open, and for some reason the search is now allowed (at least according to the Companion App).
In the EU edition(s) there was a line about how you couldn't be adjacent to a monster to search. I agree with that. So if you're in a room and you want to search the room and you're at the doorway and there's a monster on the other side, maybe I'd say sure, that stops the search somehow. But if he's out the door a ways? Who cares. I allow the search. After all, you're not searching the area of that monster, you just happen to know he's there.
I like the idea that a monster (or hero) could "take cover" in the very corners of a room (or behind some big obstacle) to hide from the missile fire or spell attacks of an enemy, at least temporarily--forcing the enemy to get closer to engage. I don't think it's so great that you have to virtually clear the whole board (rather than just the strict area you're in) to search. Others may freely disagree of course!
The EU edition had some spells (namely Fire of Wrath and Genie) that allowed you to hit monsters that were on the board, but not within LOS or even anywhere near the same room/corridor. That was cool, so their simply them being "visible" on the board was enough. But those don't really exist in the NA/remake rules that I can recall. I haven't yet implemented any "seeking" spells like this so far.
So I'm not going to worry well I can see him but I can't see him. I'm just going to ask... is he being shot at or cast upon? Then trace the unobstructed line. Is he searching? Then check the room/corridor for enemies (and don't count sleeping ones).