I have to assume that by now they have run a compression test, and that is the basis for saying you have a bad cylinder.
They should have written the actual results of the compression test someplace - whether on something they gave you or not. Would be be able to find out, in psi, what the compression was on each cylinder?
If it were me I’d ask for a cylinder leak down test. Its quite true that there are lots of things that can go wrong in the engine, but those 2.0L Ford engines are known for having bad valve seats, and the car can be fine one minute and not the next for no apparently good reason.
Because it is a fairly common issue, remanufactured heads are pretty easy & cheap to find. They are also among the easiest to install - relatively speaking. If they can determine that this is primarily a valve issue IMHO the car would be worth a new head.