It totally happens all the time, and you don't have to go as far as traditional vs. nontraditional to underline it. When I was behind the tango bar, the owner and organizer regularly asked the DJ – who was right there next to me – to play something she or an influential or popular guest wanted, or not to play certain music. One DJ I loved (and who is no longer with us, R.I.P.) told me, "I'd love to play X, but she won't have it." I'm talking about specific Golden Age music here . . . orquestas, recordings, years, whatever.
I find the claim that DJs generally have free rein to be more surprising, to be honest. Most of our local places have crowds with clear preferences, and the organizers definitely tell the DJs to respect those. Of course, in several of these places the DJ is one of the organizers most of the time, so it's less obvious.