Here's what I recommend
For starters, I too would be extremely upset if Apple avoided repairing my machine. I was quite dissatisfied with the communication between myself and Apple when I had my original MacBook Pro repaired twice, and then replaced. I never really learned what parts were repaired or swapped, nor did they fix the splitting seams on the edges of the computer. Fortunately, the Mac the manager presented me with has none of the previous problems I encountered. The Genius and manager I spoke with that day were most helpful and understanding, where the last two techs I had dealt with were not so interested in helping me out. Depends on the person, and when you get a good employee, you find that Apple's support is very good. Last time I went in for technical issues, my old G4 fried my 6-month-old WD hard drive. I had bought it there and my Mac caused it to die, so I asked if Apple could work it out. I didn't want to ship it off to WD and wait for it. So the Genius decided he would give me a new one. He walked over to the shelf next to the bar and handed me a brand new one. Nice service for me.
I had the Genius Bar handle my problems, and once everything was sorted out, I was able to happily leave the Apple Store. If Apple is claiming you have caused liquid damage to your machine when you have not, see if you can speak with a manager of sorts. If you're going to one of the retail stores, simply ask for one if you haven't dealt with them already. If that falls through, call Apple's support line and request a representative that's high up in the ranks. Explain the situation calmly and ask what you can do to resolve the problem.
1. Again, stay calm and keep a neutral tone with the employee. Has worked well for me.
2. Pray you get someone who is in a good mood. That really makes things easier.
3. Keep and record everything that has transpired and file it. As boring as paperwork is, it is very helpful to have on hand when engaged in these matters. Present what you have to the representative and explain everything in detail.
4. Try not to directly accuse Apple of anything. I would advise referring to the facts that the Air's warranty has been neglected and that so far the machine hasn't been taken care of.
It seems you have already documented some of your experience, so that will help. Here's a problem though: you say you opened your machine to investigate their claims. I would be very cautious about mentioning this. Under normal circumstances, Apple will void the warranty if you open it up. If you speak of this to Apple, be sure to have that paper handy. Someone may try to use this action as an excuse to deny you any free repair. At this point, I would press for a new machine since you have seem to be ignored. The new Airs are supposed to be much more efficient and reliable than the originals.
As some say, the consumer is always right, for the most part, so Apple should not be contesting this with you. I really enjoy using Apple products, and the company has always come through for me when I've requested assistance. For the majority of Apple's customers, things work well/great, so throwing this out into the mainstream media or court won't do much for you. I would hesitate to turn to legal action at this point; only if the situation escalates to an out-of-control level should you consider the notion. From my experience, Apple's warranty is okay, and their support is generally above average, so I doubt that you could make a successful case out of it all.
If all else fails, send a nice email to Steve. Some high school kid got a free copy of Final Cut Studio 2 a little while back (although why should a person with an 8-core Mac Pro need help buying $1200 software?). You could be lucky and Steve may take a glance at your story. Good luck.