+In light of this, wouldn't you have bought the machine under the expectation that the Protection Plan entitled you to on-site repair?+
Hmmm. I believe the "Getting Started Guide" from which you quote was contained in the AppleCare package along with the "Terms and Conditions." You evidently read it after purchasing AppleCare, although that language *is similar* to Apple's online explanations of AppleCare, so same difference.
But, in answer to your question - perhaps eligible, depending on your location, assuming the Store person was familiar with your location, but not entitled, and certainly not if I already knew or suspected I lived outside the area eligible for on-site service. (Perhaps you need to confront the manager of the store where someone gave you that promise or advice - this *is only 6 months* afterwards.)
But also no, because I did finally read the Terms and Conditions online at the Apple website prior to my first purchase of AppleCare. In 2004, when it was first offered to me when I purchased my first Mac at an actual Apple Store, I refused to buy AppleCare because just on prinicple I never buy service plans - and because at that moment I didn't really comprehend what all was included in AppleCare Protection Plan coverage. I didn't receive any sales pitch, just an offer which I refused.
Once I looked it up online and understood that so much was included, I've never since failed to purchase AppleCare (and recommend it to others) - not only for in-store diagnosis and help, as well as the excellent phone support extended from 90 days to 3 years, but also for the extended coverage that applies to not only a Mac but to accessories such as AirPort Extreme and Express base stations, Time Capsule, keyboard and mouse. While I don't know anyone who's needed to use all these things, I do know some who've received far, far more value from their coverage than it cost them.
Nevertheless, it's also been clear to me that the onsite service *might be available* if an Apple tech lives in your area, not just if there is an AASP located in your area. I've always assumed this meant such a tech calls upon you on the way to or from their work or work route, or that they may be an independent tech working "on call" for AppleCare. You might want to concentrate some of your inquiry with AppleCare personnel on these angles.
Maybe I'm wrong, but in your case I think it's worth an additional phone call to AppleCare, a complete explanation of your work needs situation, and an appeal that the person with whom you're speaking try to find some extra bit of help for you. Since in your OP you stated: "They suggested that the noise I am experiencing is not normal." - it seems that you need to emphasize that it might be best that a tech reviews the situation on-site before removing the iMac from your use. While it may very well not take 10 days till you have it back, it just might. (I had a logic board replaced 2 years ago - was told "10 days" but it was 2 days.)
While you need to be as friendly about it as possible, in the event of a negative response you shouldn't hesitate to ask to speak to a supervisor so that you can make the same direct appeal to that individual as well.
That said, have you considered the working environment? If the back of your iMac is parallel to a wall, and too close (less than 15 inches), it may be that a reverberation effect has developed that is actually magnifying all sounds that are usually limited to being emitted from the reverse side of the iMac - making them just loud enough to be picked up on the front side after they reflect back and forth (wall to iMac case) a few times.
Just to be sure, you don't have it positioned so that it's enclosed in any way, right, as you must allow for air circulation.
These sounds might be countered by moving the iMac slightly further away from whatever is behind it or by angling the iMac a bit to break down any reflective effect that might have been accidentally created by its placement.
Also, have you tried rotating the iMac stand 180 degrees so that the back of it is in front of you - and then comparing the differences? This direct study of the noise may help you understand how to counteract or at least temporarily limit the noise.
Best of luck:)