I get the privacy thing, but IMO, as soon as you refuse to allow them to do their checks, red flags go up and they now have reason to believe you're hiding something. You'll get searched extra thoroughly. If they can, they'll nail you for little things that would otherwise have been overlooked.
Ask yourself this:
Who would a judge side with ?
The guy who refused to allow the CO's to do a routine roadside check, or the law enforcement officers conducting that check ?