They are just lazy and know their own box. Tell them they have two choices: 1) Use the DI from your amp head. 2) Mike your speaker cab.
Yep. I was involved in a video taping for a local cable access channel on Sunday (same day the OP posted, coincidentally). The "sound guys" were lacking, to say the least. They put a SM58 in front of each of two HUGE PA bins, poorly placed on a ledge about 10 feet above the floor. Yeah. Fixed location, house speakers. No idea who thought that was a good placement! Mics were pointed at the lower right quadrant of the 15" bass cone, and nowhere near the tweeter/horn. Mistake #1 ... to get a decent tone on the tape they boosted the highs and mids in the room ... and it sounded awful live, and not a whole lot better in the recorded mix. Three guys worked together to get such a craptastic sound. Then 15 minutes to EQ the acoustic guitar. All the time I'm tellin' them that my bass will not be heard in the recorded mix since they weren't running my bass through the FOH (where they were mic'ing). I told him I could give him DI, pre or post EQ, line level or mic level, and had a ground lift if I needed it. Nothin' but a blank stare and a tentative nod. I finally ran an XLR from my head's DI, preEQ, to the board and handed him his end. He looked dumbfounded. So I plugged it in, set a rough EQ, waited for him to sound check the bass. Nothin' ... he was busy chatting with a guy who wasn't even in the show. Booming feedback ... I was using a Tacoma Thunderchief acoustic bass guitar, a boomy beast under ideal conditions, but I
always manage to get it to sound very much like an upright bass (what I'm aiming for) without difficulty. The "sound man" didn't know what knob to twiddle and shrugged. I finally threw a minor hissy fit ... and loudly said, "I'm not gonna sit here and play for the next hour if no one's gonna hear me" ... and started to pack up my stuff. Then remembered my emergency gig kit was in the car. I pulled out a SM57, mic'd the cab, and set up my own sound at the board. I finally got what I wanted, but had to do it myself. What a PITA.
I should mention that we weren't recording bands, but rather solo singer/songwriters, and I happened to be playing bass for three of 'em. The sound check should have been 15-20 minutes, tops ... but took over an hour. I should also say that this isn't my usual experience with professional sound guys. I suppose the amateur cable access volunteers have to start somewhere, but man, it was frustrating!