I'd put it this way, rules that tell you what you CANNOT do impede role play, or at least get in the way of character concept, and also tend to damage my sense of immersion. However, notice that 4e doesn't do that much. AD&D was far more guilty of this with all its arbitrary rules like "clerics must use blunt weapons" and "wizards can only use daggers, darts, and staves" (lul wut). Admittedly there is a matter of degree there, but it is pretty clear that the designers of 4e thought about this deeply from the start of the design phase of the game.
I would argue that character concept and role-playing are entirely different things.
I would assume that you wouldn't argue that 4e was less of a role-playing game when just the PHB was released (because of fewer options than now)? I would assume that you wouldn't argue that Top Secret was less of a role-playing game because it didn't feature elves?
IMHO, a game allows for role-playing based only on two factors:
1. Does the player get to make meaningful choices within the context of the game's fiction (noting that meaningful choices include consequences to the choices made.....talking in a funny voice while playing Silent Hill does nothing in terms of game play) through taking a particular role?
2. How much and how often do the rules break immersion in role?
The first is probably more objective than the second, as one can easily see that neighing while moving the horse in chess isn't a meaningful decision, but it is still subjective to some (and perhaps some not-inconsiderable) degree.
The second is going to depend upon a number of factors, which I did my best to outline earlier, and which also require largely subjective analysis. As noted just above (and in my previous post), as one learns the rules of a game, the game rules become more natural, and break immersion less.
With these points in mind, it is easy to see that there will not be "one true answer" or "one true gauge" of how well a game functions as a role-playing game. But, it is also true that system matters.
As a simple test of the "system matters" principle, if system did not matter, few (if any) would throw their money away on other systems. Once you tried one, you would stick with that one. Why not? If system doesn't matter, then there is no benefit to changing system.
(I also find the idea that system doesn't matter to be a colossal insult to the good folks who spend so long designing and playtesting those systems.)
RC