My problem was WORSE than yours... because I bought my MacBook Air in the US, my Apple ID, my address, my credit card, etc... is in the US, but I am currently visiting PANAMA (an Apple rep wanted to know what this was, and I had to explain it was a country... I asked if he had heard of the Panama Canal and he had not... he probably thinks Michael Jordan occupies a seat in the U.N.). That means, among other things, that there are no genius bars in Panama - which is probably not such a bad thing if you consider that the first thing some of these "geniuses" recommend is replacing the hardware, when this is obviously a software issue.
My MBA was working fine until I bought the ML upgrade. Upon installation, I had to go through all those depressing screen shots and quickly found out my HD could not be repaired. Luckily, I had purchased Apple care... The first agent (I spoke to about 8 of them in the course of 2 days) gave me the instructions to perform an Internet Recovery: hold option/command/R while turning the machine on. To do that, you obviously need an Internet connection, but for some reason my Wi-Fi didn't show up on the list and the only solution I found was to connect through my iPhone Personal Hotspot. It took 12 hours... (in retrospect, since I was about to wipe off the HD, I should have done that from the start and it would have taken less time to do the procedure with 1 GB instead of 200 GB). Eventually I was taken to a screen with disk utilities options. I called Apple again, not wanting to do something stupid... on my own. I was instructed to create a single partition, with extended journaled (don't ask me!) etc... Everything went along fine, until at the end, when I needed to insert my Apple ID. Permission was denied... Pretty frustrating, to say the least... The issue was now that the IP address showed I was NOT in the US, but I had a US Apple ID... I requested to escalate the case and apparently no one had a solution to this. I observed that Apple had no problem selling me the ML upgrade (or any other app) while traveling outside the US...
The solution? To perform another Internet Recovery... This time, as we had wiped off the system, it took only about 5 hours. After which I called Apple again... You know the definition of crazy: to repeat the same thing and expect different results. I ended up talking to another senior adviser. Actually, she did all the talking... whenever I spoke she would drown my words with non-stop chatter. She offered to provide me with her contact information and I said: "please don't" before hanging up. She had me change my real US address with a fake Panamanian address. I did, but very reluctantly. I didn't think this would fool the system. I called back once again, and this time I had a great rep on the line. He had a better idea... I had completely forgotten about that little USB key that had come in the package of my MBA... I rebooted using that recovery key. He told me that was a temporary fix and that I would need to travel back to the US to have my stuff back... Not very encouraging... OK, now my system was back to Snow Leopard, like it was when I purchased the MBA. I had make a Time Machine back up, two months earlier (not to self, do a back up before upgrading!) and of course it was on Lion, so I went to the app store and tried to download again Lion, but the only option was ML so I decided to select the new OS anyway. It worked. After that, I selected migration assistant and transferred from the Time Machine back up. I got a weird message saying that the system was preventing log out and I had to call Apple again. It took a few simple steps (the back up had created a new user and I had to select the one I wanted and delete the useless one) and now I'm back on track. Like nothing happened, except my two months of data that I hadn't backed up... Of course, you can do the same thing with a replacement HD, but that doesn't sound necessary!
Woah man. That's quite a story. Glad you got everything sorted despite the ordeal.
And I can't believe the tele-specialist you spoke with was so geographically impaired!