I dont really agree with what you determine to be a RPG, all games have a world, gameplay and story, so by your logic all games are a RPG.
In an RPG you or your parties strength, dexterity, charisma, combat ability etc. are all governed by skills and attributes, so yes a game does need stats to be considered an RPG.
The rest of your post is pure opinion, though i lol'd at "oblivion had the perfect world".
That people are so obsessed with specific ways of handling stats and the use of dice rolls is just plain sad, in my opinion. RPGs were never about dice rolls or that other nonsense, they were about simulation of growth in both power and influence as well as role-playing what you want to role-play, but due to limited technology, that was all that could be done, then. Now that we move forward and be a bit more innovative, people have this nonsensical delusion involving a "it must have dice rolls and boring combat to be an RPG" rule that, quite frankly, is one of the most short-sighted and unhealthily obsessed things the gaming community seems to defend, in my opinion. Of course, that is all just my opinion. However, in the case of attributes, all they did in Morrowind and Oblivion was tie into a horrible attribute scaling system that I am glad is gone. I think Skyrim is taking this all of this in a better direction, and I'm saying that as an RPG player.