As a few others have wisely said:
1. Whoever is paying the bill gets the final say (or is, at least, the person who you should be making your pitch to).
If you've agreed with that person on your tone, and the engineer doesn't follow your wishes, or at least explain why a different tone would mix better, you should consider taking your future business elsewhere.
2. I have a live tone which I really like. But when we record I do it 'clean', and we make the adjustments later. As others have pointed out, it's much easier to tweak and experiment with a clean track.
As faulknersj pointed out, this is probably where the engineer is coming from - and it's understandable. But not listening to the band/person paying the bill is not good practice (imo).
Also, as paganjack mentioned, recording mic'd AND a DI into separate channels simultaneously is a good and easy approach, and something that I've done before (and been happy with).
Anyway, I think the bottom line is: if the band wants a certain sound, and is paying for it, that's the sound they should get (best practices be damned).
-k