It is most definitely possible to "run bad" in Donkey Kong. For example, I go through periods of dozens of games where I'll get a free pass on conveyors maybe 1 time in 15, and the rest will just be agonizing. Then I'll snap out of it and have mild conveyors for a while. Rivets can be streaky too, as can a rash of climby fireballs on barrel screens. It all comes and goes.
Having said that, Mitch is right about the game, mixed with your brain, being extremely prone to spinning the
illusion of bad luck, especially for those who haven't gotten it dialed yet. We all went through this and, when looking at our games in retrospect, can see that we weren't actually as unlucky as we thought. We just didn't know what we didn't know! Then you gotta factor in selective memory, etc.
The truth is somewhere between the two - it's almost always less bad luck than you think, but more bad luck than anyone else will give you credit for.
As for the question of this thread, I feel that, due to the inevitability and regularity of totally no-fault deaths, and the fact that everyone has momentary little boneheaded brainfart screwups that they simply can't 100% prevent, just about *everyone* is better than their high score indicates when it comes to pure skill. And it becomes even more true the higher your pace. (Higher pace = more randomness.)