Omega's warranty does mention shipping is covered for warranty repairs. So it's safe to say some brands cover shipping charges and some brands don't.
Patek warranty doesn't mention it. So we cannot assume it's covered. So, by contract, there's no obligation for neither Patek Service Center nor the Boutique to cover it. The original poster had an expectation that was not grounded in fact. Simply based off his own expectation that a luxury brand should cover shipping costs for a warranty claim. We don't even know if the diagnosis of the watch qualifies for a warranty claim.
My first watch, a Patek Philippe, was sent in for a small bracelet problem (a screw was stuck, probably too much Loctite, the screw wouldn't come out) when the watch was brand new - I had purchased it but the bracelet had not even been sized yet. I was not charged. I did not expect to be charged for a problem that I considered so obvious was Patek Philippe's mistake. But, the warranty did not specifically state that shipping would be covered. So if I had been charged, I would've been unhappy, but I could not say I was unfairly treated.