Cases like this are precisely why I buy the 3 year extended warranty. I'm perfectly capable of replacing stuff myself, but the piece of mind you can buy is worth the money.
In regards to your case, it could be looked at either way. From Apple's perspective, there is no way for them to know what you did to your machine. For example, perhaps you left this computer in your car on a sunny day after using it and this caused some component in the battery to react badly due to being left outside the normal operating temperatures. I'm not saying you did something to your machine, but from Apple's perspective this is a possibility.
On the other hand, from your perspective, this could be the result of something that was wrong with the battery from the point of manufacture that is manifesting itself 18 months after assembly.
While you have had bad experiences with Apple, I must say that so far I have had great experiences with not just Apples customer care but their products as well. My advice to you would be to call their customer care center for a second or third time and present your case to the operator as you have on this thread. I suspect you've gone through the iterations so many times that you'll be able to present a compelling case to the Apple people and Apple will come through with the legendary customer service. I'd use gallons of sunshine with a brief mention of your talking about the problem on macrumors inserted in there somewhere. Good luck, my friend!
PS: Let us know what the outcome is!
Agreed. I skimped on AppleCare once and got burned (fried logic board in an iBook G4 - they wanted me to pay $1000 for the repair!). Never again.