Hi.
Like said before, all DI's are not created equal. What may well be the problem here (aside of the obvious "small system syndrome"), is that not all mixing desks are created equal either. Some don't have pad's at all and he is afraid that if You at some point feel that you need more volume and/or EQing during the show (always a bad idea IME) he may run out of gain reduction.
Edit: "a special attachment" does sound a bit like a "special attenuator" doesn't it
If the sound engineer doesn't have that much confidence in You and vice versa, there's something very wrong in your "relationship".
A separate outboard DI-feed is always the easiest solution for everyone involved, but not always the best

.
What always is left out in rants/vents like this is the size of the show, number of bands, and most importantly the professional level of the gig.
For example: BOTB, sub $500, $500-$1000, $1000 and up.
Or the entrance fee: free, <$5, $5-$15, $15-$30, >$30.
Or: a backyard party, a bar gig, a festival gig, a corporate gig.
You get the point?
Everyone naturally gives pointers and opinions with their level in mind (mine's sub $500 ATM) and also leave that to be guessed. Granted, the people who reply simply can't explain every time a question like this comes up (bi-weekly?) what's their level, but I feel that it's not too much to ask from the OP's.
Regards
Sam