I don't deny that it is an action-RPG, but the "Morrowind is an RPG while Oblivion is an action game" claim is what I dislike, and you do not disagree with that, do you? What about the "Morrowind's combat is character skill based while Oblivion's is player skill based"? Do you believe that Oblivion is in a different genre than Morrowind? By action-RPG, you're still acknowledging that it is an RPG and not an action game(not a pure action), are you not? I only care about the unfair claims favored towards Morrowind that you also seem to disagree with, for the most part, because I agree, the entire series is a sandbox action-RPG series, but I don't agree that, somehow, Morrowind is an RPG while Oblivion is an action game that's all about player skill and reflexes.
I would call them both an action-rpg, not an rpg and an action game. Part of that comes from "hardcoe" rpg fans being a very, very bitter lot. While the targets are not always deserving, the bitterness is warranted, which makes it a difficult argument to cool down. I would say that the non-combat factors of Morrowind and Oblivion are rather flimsy, but that flimsy implementation is still better and stronger than most other supposed rpg's on the market (although the definitions of the genre really are vague and awful). Dragon Age: Origins, for example. I never see it called an action-rpg, just an rpg, yet it's more combat-heavy than the TES games. Non-combat elements are barely there. Sadly, "true" rpg's simply have a weak grip on the market, so those features don't get much emphasis. Rpg fans and their games were once the darlings of the medium, with incredibly expansive pen and paper games and videogames that worked hard to duplicate that experience, because they were able to focus on that niche. That was years ago. Now those fans are pissed off by years of being ignored and having to settle for "action games with rpg elements" and the like. TES has stronger elements than other games available so they cling to the series desperately, and when one game from the previous does something to weaken those elements, such as fewer skills, they go berserk like long-abused dogs in response to a finger coming in to jab them one more time.
I wouldn't put them in separate genres, but I do see a difference. Not so much a greater emphasis on action, but a lack of effort to stand up those faltering rpg elements. There are fewer skills, and mini-games that reduce the value of several others...which may draw extra nervousness considering that skills lost in the past were largely "not valuable." Combat does not require more player skill, but does involve less character skill. However, this difference seems larger than it is partly because of that same bad scaling feature. If you a warrior character based on the skill, raising it will increase your level, resulting in tougher and better-equipped enemies. In order to feel like your increasing skill is giving you an advantage you have to raise it as a minor skill, which is not good. Plus, if I understand the http://www.uesp.net/wiki/Oblivion:The_Complete_Damage_Formula right (which I probably don't, I hate you math), the quality of your weapon has a larger impact than your skill with it. You're likely to find better items faster than your skill increases,
especially if it's a major skill that's also increasing your level, further dampening the benefit.
Overall I don't consider there to be a large difference between the two games as far as how "RPGable" they are, but do think that in the difference that is there, Oblivion moves farther away from it. That's all it takes to make a lot of people see red.