What you're essentially saying when you say an mma fighter beats a boxer/kickboxer/jiu jitsu fighter under mma rules is that an mma fighter does not have enough skill to beat a guy in a single discipline and can only win if he has an advantage at one thing or another over the other guy. If it stays up the pure boxer/kickboxer/muai thai (striker) wins. If it goes down and stays there, the wrestler/jiu jitsu guy wins. Pure artists have more skill than mixed ones. FACT.
Yes of course. Jack of all trades, master of none. Its called MIXED Martial Arts. Thats why I don't like the Boxing(or any style for that matter) versus MMA debate. There's nothing to debate about, each is very different with the exception of ONE element, and in the long run all we get is everyones personal reason why they don't like one or the other, with no gratifying truths.

Maybe if you read this quote from Bruce Lee you will realize what MMA is.

"To set the record straight, I have NOT invented a new style, composite, modified or otherwise; that is, set within distinct form and laws as apart from "this" style or "that" method. On the contrary, I hope to free my followers from clinging to styles, patterns, or molds. So do remember that the term Jeet Kune Do is merely a name used, a mirror in which we see ourselves. The name brand is nothing special."
He knew what it was, and that was back in 1965. Its not about being the best boxer/wrestler/kickboxer in the world. MMA is about beating your opponent, and becoming the best FIGHTER possible. Not to be confused with the best ARTIST possible. And thats why I love it.