If the oil was completely drained from the car, and the lube "tech" didn't check the level before you left, it is possible that the oil was low. Not knowing that the oil cooler was there means the tech probably put the "standard" amount of oil in. With an oil cooler, you of course need more. Unless you have a big oil cooler though, 3 qts is a lot.
If they can't show proof of an oil leak, then it's their fault for not putting the correct amount of oil in when they changed it last.
With all this tomfoolery, I'd have the car taken to another dealership. They seem intent on blaming you for the issue so who knows what kind of stunts they'll pull to put this on you.
Good luck
