I don't know what you think Gygax mean by "abilities". Given that ability scores in AD&D do not generally increase with level, I don't think that's what he mean. I think he mean the various class abilities that are gained with levels; and in 4e D&D these include a level-based skill bonus.Right. Gygax wasn't talking about skills. Abilities =/= skills. You are conflating saves and hit points with skills when it doesn't apply.
When it comes down to it, both sides are correct in this. I makes sense and is correct for someone who is quasi-divine to have innate skill in everything if you want it to be that way. It also makes sense and is correct for someone, even divine someones to be poor at skills they wouldn't have. Thor disguised himself and could be stealthy, but he wasn't a thief or academic so sleight of hand and arcane knowledge were not things that he would have any skill at. You can go either way and have it make sense if that's how you want to structure the fiction.
As far as "what makes sense", I am not making any claim about that. People can imagine whatever they want to. What I am saying is that, in 4e, it is not at all ambiguous why high level PCs have strong skill bonuses, and it is nothing to do with "passive learning". The PCs are capable because of their will, their power and their affiliation to supernatural forces. The whole structure of class build - Paragon Paths and Epic Destinies - as well as the description of the Tiers of Play, and the rest of the flavour text, makes this clear. And it gives effect to an idea that was first set forth, in the D&D context, by Gygax, in the passages I quoted.