Marilyn,
I have no intuition to argue with you about your experiences with Apple. I would, however, like to explain why I made some of my comments. And some of them were not even addressed to you but other posters on this thread. That is normal at Techsurvivors and sometimes it gets very confusing trying to follow the discussion! I'm probably one of the causes of much of that confusion!!
I think there may have been some confusion about who and how the "replacement" item was to be obtained. I thought you said Apple wanted to repair the original Air. That is usually their initial method. And that would, indeed, be covered by AppleCare. But when you decided to return the Air for a refund, graciously offered by Amazon, there was nothing for the registered AppleCare to cover. Thus it became null and void. It applies to a particular hardware item and there are specific plans fro several different items. That is, you can get AppleCare for an iMac, the Air, the MacBookPro, for example but they will all be differently priced because of the different environments they operate in and the expenses of repairs. Same goes for iPads, iPods, iPhones. While they can be transferred to new owners of the particular machine, they do not and can not be transferred to another machine, even if it is identical to the original one.
Many people, myself included, often recommend buying the Apple-refurbished products. The reasons being that they have already had 99.9% of any problems found and fixed. Electronics tend to either run forever of fail soon after purchase. Apple's refurbishing saves a bit of money, much more than any price of a new machine from any retailer (including Apple) but the other advantage is that the machines are still eligible for AppleCare!
AppleCare is an extended warranty, not a replacement guarantee. On the other hand, I must say that Apple has often made a replacement available, with or without AppleCare being involved. Often these replacements are offered well after the AppleCare warranty would have covered the item. In that case, obviously, there would be no continued coverage. I have no experience with what happens when an item is replaced,
by Apple, during the period covered by AppleCare.
I still think Apple did a bad job of helping you with your problem. But I have had lesser problems badly handled by them, at least once. But that problem was a matter of getting the problem explained (from my end) to some one who could offer the solution (at their end). Eventually, in my case, I went from the "Live chat" system to the email system to a phone call with a real person. I appreciate your ability to avoid becoming angry, I have that particular problem, myself!
Finally, I'm just glad you got back to "square one" and can now move on to more enjoyable pursuits. One of which I hope will be visits to TS! No matter what our experience level, everyone can be a help at some point!