Radiator Flush

Is the car running poorly or is the head gasket diagnosis given only because of an overheating problem?

Offhand, it sounds like the fast lube erred in filling the coolant. The mistake you made was continuing to drive the vehicle while it was severely overheating.

I would be very leery of a head gasket diagnosis fault that was given to you by a fast lube facility who got their information on a phone call from a service advisor at the Subaru dealer. Most service advisors are not sharp, mechanically speaking, and I have no idea what this alleged safety device is that the advisor refers to.