Sounds like this Muffler Mechanic is describing warped headers…yes they can damage a cylinder head if driven with a high velocity leak at the head…but methinks this is just a guy who is trying to repair a leak and working with what he has to work with.
A warped header and doubled up Exhaust Man gaskets will or should put this to bed. Then again… a new Ex Manifold wouldn’t hurt if the old one is warped or cracked…I mean that is how you fix this sorta thing.
Also attention needs to be paid to how the downpipe is attached or not attached to the rest of the vehicle…this is why there are so many “Flex Pipe” sections out there these days. Some mfgs use normal exhaust pipe in the design and then “isolate” the rest of the system with rubber hangars…others are forced to use those stainless steel flex sections to allow the engine some literal “wiggle room”. Not sure of your exhaust makeup tho…Id have to look it up but you do not want the exhaust system to apply forces to the exhaust manifold unnecessarily.
Once a header warps at the head it makes noise…enough noise for you to stop and take a look and not continue motoring… My money is on the manifold or the studs in the head or lack thereof being the real problem…replace whatever is warped or broken it and it shouldn’t be suspect anymore and I would HOPE that is not referring to the head.
I think they told you this because they replaced the gasket on a manifold that was warped, cracked OR the dude broke 3 out of 6 manifold bolts in the process of removal and now knows its held on by the skin of its teeth…or something like that. Wouldn’t surprise me in the least little bit. You need to have a looksie…if it all looks normal and all bolts / studs are present…ask him why he told you what he told you. I doubt the head is damaged Port Wise… Could be Stud wise or thread wise…