It's uncommon, but there's nothing stopping heroes from attacking each other in the NA version (it's happened in a couple of my groups). There's also no rule stating they have to divide their gold treasure, only the reward in the quest introduction is often divided, but this is still only divided among the surviving heroes. Most often, the gold treasure found during the quest remains the prize of the hero who got to it first.
D'oh! You're right about the treasure. That's what I get for making sweeping generalisations... I was only thinking of the reward at the end of the Quest, not treasure searches--but even in the EU version, often every Hero is rewarded rather than just one.
I also just went back and read through the NA rulebook again, and you're right, it doesn't explicitly forbid you to attack other Heroes--it seems to assume nobody would ever be so unscrupulous as to need forbidding
I do note, though, that the NA version says Heroes can move through other Heroes, whereas in the EU version you have to get permission from the player controlling that figure. This was the cause of many a kerfuffle in my games, especially in Quests like Bastion of Chaos when everyone's racing one another to kill stuff for gold. Wizard cruelty potential: high.
I may be a bit vague on the particulars because I lost my EU rulebook sometime in my childhood and could only find an NA rulebook online to replace it back in the day, so my memories are a weird blend of both, plus our own house rules. As you say, it's one of those games that everybody plays differently anyway. Like Monopoly, only with less violence. (That old chestnut about asking to open treasure chests vs just searching in the same room, for instance...)
The EU 1st edition book appears to have been a bit more blatantly competitive than the 2nd edition, too. They seem to have toned it down a bit after that. I've only skimmed through the 1st edition online, but even the learn-to-play sections involve fighting the other players to the death...
(This is all probably a bit rambling for what's basically a 'hello!' thread... sorry!)