/snip
I suspect the meat of the disagreement in this discussion is found in that #6: that really a lot of the difference in opinion comes down to where we come down on that question. And it's another spectrum thing: it's a smooth continuum between the two extremes, and probably few or none of us are all the way on one side or the other. But leaning more toward one side or the other probably correlates pretty highly to some of the opinions expressed here.
But, at no point was the decision process not being filtered through the character. It's not like having a personality is a straitjacket that you can never vary from. Of course not. But, that being said, if the character is defined as cowardly, and then NEVER acts cowardly, then that's not really playing that character. If the character is defined as whimsical and impulsive, but never, ever acts impulsively, is always reliable and is 100% tactical all the time, then that's not playing that character.
I'm not even really talking about that to be honest. So long as the character filter is present, then you are role playing. Ignoring that filter is role playing badly, probably, and is generally frowned upon or at least seen as a form of degenerate play, but, at least the filter is actually there.
I'm talking about pure pawn stance where there is no character AT ALL. Your character isn't brave or cowardly or anything. It's just a bunch of numbers on a sheet and there is zero filter between the player and the game world. This isn't even a case of someone playing themselves in the game world, since, frankly, that happens so rarely. Very, very few players are playing a modern 21st century human in a D&D world. No, they are playing a fighter (or whatever) that overlays their own personality. Fair enough. Again, at least there's a character filter there. There is a distinction between the character (me+class+setting) and me (21st century human).
Yes, I realize there are examples where you are just playing yourself in a fictional situation. But, that's a pretty corner case and we can largely ignore it as a special case in and of itself.
But, if you are filtering your decision tree through the filter of that character, then you are role playing. If that filter doesn't exist - then you aren't. I don't make decisions in Magic the Gathering based on what a centuries old Planeswalker would do. I make decisions based on whatever strategy I think will win. I don't have to try to inhabit the head of a Tyranid in order to play Warhammer 40k and those games certainly don't expect me to try. The game certainly never expects you to run away in Halo and won't even allow you to do so. So on and so forth.
Frankly, I'm a little surprised that my definition is getting this much pushback. I wouldn't have thought that "in a role playing game, you play the role of a character" was terribly controversial.