That's too bad. Here in Japan Apple sends a courier with a specialized shipping container to the customer's door and overnights it both to and from the service center in Tokyo. You just hand them the iMac when they ring the doorbell.
Also, I've had a few service calls under AppleCare over the course of my 11 years as a Mac user, including expensive LCD panel replacements and Apple has never refused service once.
Are you in the US? I'm an American citizen living long term in Japan and I can say that service is just generally poor in the USA in comparison, period. I can't speak for Apple US specifically.
That's nice....
Apple will not accept a 27" iMac being sent in directly to them in the USA.......
I have a Late-2015 that has been crashing on me and I've had it to the Apple store multiple times......the last time I wanted to send it back to Apple to work on and they said it's not possible and they won't accept it on the large machines.
But, it's OK for us to lug them through a shopping center mall to the Apple store multiple times.