Words mean something, … or at least they used to……………
Basically, I agree... but it's worth noting that language evolves to meet new perceptions of reality.
Notice I say PERCEPTION of reality... all that's required for the dictionary definition to change is for most people to perceive a DJ as a musician.
Sometimes it’s wise for people knowledgeable in a particular subject to override perceptions or even dictionary definitions and speak out in order to educate others.
Take for example the Meriam-Webster dictionary definition of a luthier:
lu•thi•er
ˈlo͞odēər/
noun
a maker of stringed instruments such as violins or guitars.
I could go to a website like “Build Your Own Guitar” and order any number of kits and easily build my own electric guitar inside of a week. Shucks, … if I were willing to fork over $525.00 for a USA Made Natural High Gloss Tele Kit – Flag, I could make an instrument that would rival the USA Fender Telecasters being sold at music retailers all over the country.
http://www.byoguitar.com/Guitar_Kits/Guitar-Kits.aspxI've been working on guitars as long as I've owned guitars, and that's been about 45 years or more. I’ve disassembled, cleaned up and reassembled several electrics over the years. I’m also pretty good at setting up guitars for proper intonation, string height, neck adjustment, sanding frets, filing nut slots, etc. Did I mention that I'm also a pretty good carpenter?

So if I purchased one of those kits and built a guitar, then I would fit the textbook definition of a “luthier”. Especially since I could easily build an instrument worthy of the components supplied in any of the kits.
But only a fool or someone who’s totally ignorant of what the term actually means would call me a “luthier”.
That same principle applies to anyone who would call a DJ a “musician”.