They did what they described as a "pressure" test. Said they "hooked it up to the machine" and pressure came back fine. That was on the coolant system. When you say compression test are you asking about engine compression? I'm assuming that if there is some sort of leak that is allowing coolant to seep in then compression would be lower, no?
Sounds like the service advisor is either making shit up or is just a moron, honestly. He's confusing two pieces of equipment: 1) a flush machine, which is basically just a fluid pump that you hook into the cooling system. The machine's pump shoves new coolant in one direction as the engine's water pump pushes the old coolant out the other. 2) A pressure tester, which is just a hand pump (it resembles a pump for something else that can be purchased at an 'adult' store...) with different adapters that allow you to install it in place of the car's pressure cap.
The pressure tester has two functions. One, it allows you get the system up to maximum pressure with the engine off and lets you to find external leaks pretty easily. Two, it allows you to observe how long the system holds pressure. Any leakdown should be very, very slow.
Given all the symptoms described, I would wager that there is an internal defect in the engine. Head gasket is possible, but it would probably be from an installation issue rather than being 'blown.' It could also be a crack in the head or cylinder liner. This is assuming it's being burned.
I would want to see them doing every damned test they can. Notably-
Compression test. All spark plugs are removed and the starter is cranked for a few compression strokes on each cylinder. A gauge measures the peak pressure reached. Even with something as severe as a cracked block, this may be inconclusive.
A leakdown test. Similar to the first, but a regulated supply of air is hooked up to each cylinder (engine is not moving) and the reading taken is a measure of how fast the air is able to escape the cylinder.
Those are common tests that any mechanic should know how to perform. Past that, the next thing I would do is check the coolant for combustion gases. It's a pretty simple tester that uses a fluid that changes colors when hydrocarbons pass through it. You can also use an exhaust gas analyzer (tailpipe probe) for this.
What would be even harder to get them to do, but IMO probably a good next step if NOTHING is found via the above- send the oil off for a lab analysis.