Here's a very possible cause.....
You may have had an injector stick open, forcing a lot of raw fuel into one of the cylinders - enough to make the engine hydrolock. Also, a cylinder could have taken in some coolant somehow (like a headgasket, intake gasket, etc) resulting in a hydrolock condition.
Why not remove all the spark plugs and see if you can turn the motor over then. If the motor is hydrolocked it will turn over after the plugs have been removed. This happened to my daughter's 3.8 Intrigue. Even dumped quite a bit of fuel into the catalyst.
If they read the trouble codes they will most likely be able to tell if a cylinder had a misfire and work from there. I don't know why they won't read the codes for you - it only takes a minute! Do you trust these guys? It kinda sounds like they lack experience. I sure would have checked for hydrolock before telling a customer it's seized. The GM 3800 is almost bullet-proof. Maybe you should get a 2nd opinion.
Then again - maybe they are right??
Good luck and let me know what happens.