MMA fighters don't "bash" tradition. However, MMA is all about weeding out ineffective techniques. You won't find an MMA fighting saying, "If I wave my hands around in the air, I can knock someone out". Guys in gis, on the other hand:
http://www.youtube.com/watch?v=_Z0_n7tGnK0
http://www.youtube.com/watch?v=gEDaCIDvj6I
Now these guys are outliers, but what you find in "traditional" martial arts culture is a willingness to accept things that can't be proven. It's a cultural thing, and I think that's where a lot of the friction lies.
However, many MMA fighters, or even people who have migrated to MMA as a training medium (yours truly), have spent time in traditional systems. Guys like Georges St-Pierre, Bas Rutten, Anderson Silva, Ben Henderson, and more have come from backgrounds that would be recognized as "traditional" martial arts. Some local MMA gyms offer classes in things like Wing Chun Kung Fu and Kali. It's hardly like MMA and "traditional" martial arts are mutually exclusive. I think the big difference is that if you show an MMA-oriented person that something is effective, they'll use it, no matter where it comes from, but if you show a die-hard "traditionalist" that something outside of their sphere of learning is effective, instead of going, "Wow, that sweep from Butterfly Guard is really effective, I'd better learn it in case I'm ever taken to the ground," you get, "I'll never got to the ground in a real fight because I don't want to," as if the laws of physics don't apply to them, and that guys who are REALLY GOOD at getting people to the ground and mauling them there don't exist. It's a loyalty to style that becomes almost cult-like in some cases, to the point of denying that one can learn something from other systems.
Again, this doesn't DEFINE "traditionalists", but you're more likely to find that mentality in someone who identifies themselves as "traditional".
But back to your original post. Can you learn how to do something really, really well without going to a "traditionalist"? Depends on how you define "traditional". Is wrestling traditional? I'd argue that it's the *oldest* tradition. How about boxing? Even Queensberry rules pre-date most karate and TKD systems, so by virtue of being older, is it "traditional"? Modern Muay Thai, Judo, Sambo, and Brazilian Jiujitsu tend to have a focus on sport competition; some people would say that they're not, or no longer, "traditional". Some would disagree.
You also have to realize that the majority of extant martial arts have to be modified for MMA. The classic bladed boxing stance leaves you open to leg kicks, moves in BJJ, Judo, and Sambo that use the gi have to be modified or abandoned, and so on. So your example of learning kicking from a "traditionalist" who has "done [it] for years" only works to a certain extent. I've got a buddy who's great at Olympic-style TKD- a former national champ who was an Olympic alternate back in 2000- but he's honest with himself enough to know that if he tried to kick in an MMA contest the way he kicked in a TKD contest, he'd get taken down in an instant. You can also teach someone good kicking, punching, etc. without having them go through what would be recognized as a "traditional" venue. So you actually *could* (and some people have) develop skills without going directly to a "traditional" source. Now you could make the argument that all techniques come from sources that are identified as "traditional", but if you want to take that road, I'd say that MMA is the MOST traditional, since it can be traced back, in spirit, to Pankration, which existed in ancient Greece.