That doesn't make any sense to me. Yes it may be drivable, but that shouldn't matter. If you drive it when it's only covered by storage insurance and you get caught, you're fucked and it's your own fault. I don't see why it's any of the BMV's business.
I don't know man, that's weird. Maybe see if you can get a hold of another agent? I have Grange insurance, and it's never been a problem for me.