I'd be pretty angry if I were in your shoes too. I don't think that guy had his facts right. As far as I remember, if an apple store or authorized repair place is beyond xx distance away, they will have you send it in. Call again, save the hassle of the rep telling you what you already know and tell them that you've already confirmed there' a hardware problem. Then, as is suggested all the time, calmly but firmly explain that you can't take the machine in because of the distance.
Also, if I were you, I'd pour over the warranty that covers the computer and throw any of that you can at them as well. Telephone service around the world is the same: if you know more than them, you'll have the better argument - you'll at least get a manager!
Too bad you're having this problem. Apple's rep with customer service is all show anyway. They're as crappy as the next corporation... But they do make good computers...usually!
YT
BTW: If anyone's been in touch with apple recently, they really do push the extended warranty - they're way over the top with it too. I even got 3 separate calls from apple trying to sell it to me just because I let it slip during a conversation about another computer that I had recently purchased a macbook.