Blown head gasket? (Decent compression numbers but cooling system doesn't hold pressure, no external leak)

I have a Mazda MX-5 and it was overheated due to the water pump belt failure. I replaced the belt afterwards and the car drove fine. I brought the car to the shop and they told me it has head gasket problem because cooling system does not hold pressure and no external coolant leak. They told me the compression numbers don’t mean anything. Here is the detail about the car:

The good:

-Compression number across all cylinders are decent (175 psi)

-No loss of coolant when I was driving the car daily after the overheat issue (I monitor the fluid level at the overflow tank)

-No external coolant leak was found

The bad:

-Cooling system does not hold pressure

-I needed to top up the coolant overflow tank after the car sat for 3 weeks. I only drove 300 miles since the car was overheating. I drove 150 miles, then the car sat for 3 weeks, and I drove 150 miles more. No loss of coolant was observed when I was driving the car around town during that 150 miles period.

I don’t understand why the cooling system doesn’t hold pressure. If the coolant is leaking into the cylinder, I should have bad compression numbers, right? Do I really have a blown head gasket?