Randomness is something that happens on top of that, and at extreme levels, is actually antithetical to both "player skill" AND "character skill".
This is Sawyerfag logic. There is no such thing as player skill without randomness (I'm talking about intelligence here, not reflexes). Randomness is a simulation of risk in RPGs. Without risk, there is no such thing as taking calculated risks, making meaningful choices or contingency planning. Without randomness, there is only predictable outcomes to obvious choices, no skill.
I'm really looking forward to tackling Serpent in the Staglands as Whalenought seems to realize that without a nice degree of randomness, combat is simply non-threatening.
And in an action-RPG, it's not very fun when you play skillfully but lose anyway because you keep getting bad rolls.
This is why popamoles (twitch gamers with low intelligence) always complain about RNG. It often voids what they are good at, while giving them something that they are not mentally capable of working around.
What makes someone low intelligence for wanting skill to win in a game? "Twitch" is skill in addition to intelligence. You have to outsmart your enemies in addition to being coordinated. That is how it works.
I play boardgames. There are tons of euros with little to no luck. There are tons of games with luck. Are you trying to say that people with low intelligence would be winning the games that require only skill(euros) while they would lose the luck based ones because they can't outsmart luck?
You can attempt to mitigate some luck, but in the end, if the luck is bad enough, all plans are wasted. There are people out there that only want skill based games. I find that the people that support your point of view are the same people that would never win a skill only based game and need luck to occasionally win.
I don't think it's fair or accurate to compare boardgames with computer RPG's because boardgames (like for example chess) are not usually based on numbers, have simple rules and pit you against an actual human opponent. RPG's are on the other hand meant to simulate combat between individuals. And combat is all about risk. Choosing between combat options in a good RPG system is deciding which risk you can afford to take.
For example, in a game, your character is near death. He theoretically could either heal or attack. If the enemy has 20 hp left, and your character does a fixed damage of 25, and attacks are guaranteed to hit, the only obvious choice is to attack and kill the opponent. If the enemy has 20 hp left, and your character does a fixed damage of 10 on the other hand, and attacks are guaranteed to hit, the only obvious choice is to heal, as you have no chance of killing the enemy before it kills you.
Now on the other hand if your character does 15-25 damage, can miss or critical, and the opponent can miss or critical as well - now you actually have to figure out what is the best option. You could heal, but your hp gain would also be variable, and the enemy might still kill you with a critical hit. You could attack, but the results depend on your chance to hit, critical chance, damage range, all of which you have to factor in. This is the "thinking power" that popamoles and Sawyerfags alike both lack.
I'm not arguing that twitch gaming doesn't also involve a sort of mental processing. Just that this is not the sort of mental processing a good RPG combat system is based on. That being said I think skilled twitch gamers command significantly more respect than RPG players who like dumbed down RTWP and TB systems who have neither the reflexes for twitch gaming nor the intellectual power to cope with RNG.