So my mid-2011 27" iMac with AppleCare just started showing signs of this problem. After reading about it and speaking to an online rep, they insisted I had to take the computer to an Apple store for service (saying an in-home service was not an option).
I live in the city of Pittsburgh -- so a major metro area -- and as I started packing up my computer and realizing that I wasn't keen on lugging around this massive compouter for fear of damaging it, I decided to take a look at the AppleCare Protection Plan booklet to read the fine print.
If you flip to page 20 in the AppleCare Protection Plan booklet, it reads:
"Onsite service is available for many desktop computers if the location of the Covered Equipment is within 50 miles (80 kilometers) radius of an Apple Authorized Onsite Service Provider."
So I just now called Apple support, read this sentence word for word to the rep on the phone, and he acknowledged that I am indeed eligible for this service. Naturally, there aren't any AASPs in Pittsburgh, so I have to take it into the Apple Store. I'm frustrated by this, but I wanted to share this fine print with others on here -- hopefully you can use it if Apple resists your request to have an in-home service and there is a nearby AASP.