I have not seen it happen, so I have to answer in principle.
In principle, such things can be explained by the rules used. The one whom the rules fit the best, has a significant advantage that can exceed the advantage of longer training.
Of course, I mean both the rules of the match in questions, and the rules that each combattant is most experienced with.
One interesting consequence of it is that the martial art with the less limiting rules should benefit. Aikido is way up there
I have seen it. I've seen guys with much less training take out much more experienced opponents. They do it by taking them out of their element. I've seen guys with 0 MMA training, walk into the ring and destroy guys who have spent years training just for mma. Why did they win? Strength, aggression, pain tolerance, etc. Look at the begining UFC for good examples. Nobody was training for the UFC, so nobody was prepared. What mattered was not the rules (they were almost non-existant) but if you could force your opponent to play your game. If you can do that, then you win.
This is the area bjj used to excel at. They can make people play their game. People are wiser now, and it is tougher. This is why I'm a fan of judo, most people will clinch with you without hesitation, then you throw them and have your way with them.
You speak of rules, yet refer to aikido as having no rules. While this is true in theory, in practice if you look, this is not true. Can you eye gouge your partner? Can you break his arm? Can you kick him in the groin? If you look, truly without sparing there are more rules in what you can't do. If rules are truly the limiting factor, then it is an easy fix to make the best martial art. I of course do not believe this, I think it is the method of practice, not the competition rules that make a good fighter. judo, boxing, mauy thai, some karates, bjj, etc all have great methods of practice that lead to very useful and quickly developed (years instead of decades) skills.