Not every drop of oil inside of an engine drains out when the drain plug is removed.
There is about a quart of oil tied up filling the oil passages, priming the oil pump, coating the interior of the block, etc.
If 1 quart drained out, there was enough oil in the pan to wet the sump at least intermittently, and quite likely enough to maintain oil pressure.
The sump is extremely close to the bottom of the pan, and given the fact that you cannot drain the circulating volume of oil (you can only drain the reservoir, about 4/5ths of the total volume of oil) you can assume that there was just enough oil in the pan to keep the sump wet and maintain oil pressure.
Yes this oil has probably been cooked.
No, it wasn't good for your engine by a long shot.
But did it toast your engine? Not likely. If the low oil pressure warning never activated, you're fine. The noises were probably caused by the oil foaming. I'd say your son caught their mistake just in time.
There's no need for any compression test. Unless you have documented a previous compression test, you have no baseline to determine if there is a loss of compression, unless it has such an obviously low set of readings that you would have felt power loss anyway. Without instruments telling you so.
If significant engine damage occurred, you'd experience a remarkable, immediate loss in power, accompanied by a distinctly different exhaust note.
Indeed, if you actually experienced a continuous loss of oil pressure, the engine would have lost a significant amount of power in a minute or so, and seized completely by 5 minutes or so.
The dealership should have to eat the cost of replacing an engine just for being stupid. But I'm very confident that your engine handled the abuse with minimal wear.
If you want to examine anything, examine the cylinder walls with a bore scope. If they aren't absolutely trashed, then nothing, and I mean nothing in that engine is damaged. Also, compare documented fuel economy before and after the affair. Damage will manifest itself in the form of significant loss in fuel economy (ie greater than 10%). But time will tell for sure. If it makes it 5k more miles, it will make it 100k more miles. Just be sure to change the oil more frequently the next few oil changes to help flush out the foamed up overheated oil from this botched oil change. And steer clear of that dealership.
If you want something done right, you have to do it yourself.
-Fleet manager and primary mechanic for a construction company with 10+ vehicles, for 10 years.