As has been said, you won't get instant pressure just cranking it briefly. It takes a bit for the pressure to reach the sensors and guages. I would give an engine 5 or 10 seconds before assuming the worst, but be careful, bad things can happen Fast!
It makes sense to me that if the pump lost its prime, in combination with a clogged pickup screen, the pump could have sucked a sketchy or old gasket right off of the pickup flange and there goes your pressure... crazy, but possible.
I may have to pull my pan just to check this, clean the screen and change the flange gasket.
Good luck and don't let them shake you down. A bit of knowledge gives you some leverage in a situation like that.
Sounds like the guys here know what they are talking about and really want to be helpful. Kudos to you all.