'But are they musicians' my take
Okay, so I am a musician, and I really admire these guys for their amazing skill and dammn it it gets your ass moving, which is one the primary goals of music anyway. But the age old questions is "are they musicians"? Well, there are some clues in the movie, there is a point where Mix Master Mike is talking about how he and some friends are immitating are playing horns and drums and he says "we sound like an actual band". Meaning he never thought of himself as a musician up until that point and not only that but can he make music using a snippet of trumpet better than somebody actually trained in the trumpet? I have heard djs scratch trumpet stabs (a la Kid Koala) into solos and it's kind of funny as a novelty, but honestly it sounds a lot better with the actual instrument.
Also, I have had experience playing with a DJ and he had all these little noise making devices, but that's all he could do, is make noise, he had no real idea of how to play along with a certain scale or chord progression or whatever.
So really these guys are more or less musicians, but I would classify them as extremely sophisticated percussionists at best, mixing is a whole other thing. But then again I suppose nobody has a problem calling a drummer a musician, but ask 99% of them about theory and they will look at you with a dumb look. They know bars, if you're lucky.
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"Surrender Dorothy!"