Thanks for the posts and information some of you have given me. I know some of you have pointed out that if I didn't check my oil each time I filled up my car that I am liable. If that is really the case, which per the owners manual, unfortunately I am I suppose. I certainly did check my fluid levels and maintain my car very well.
Bladecutter, thank you very much for the information you have given me, specifically this:
"Third, and this one is really important, if you had been neglecting the car by not checking your oil level, there would be sludge and carbon deposits in the cylinder head area from oil that was abused, and circulated. The inside of the oil pan should have baked on oil carbon all over it.
If your engine was spotless inside, then you need to push back and say there's no sign of neglect or abuse, and they need to fix it."
The service manager at the Honda dealer is trying to help me get it covered by putting in a good word for me with the district manager. As I think I mentioned earlier, when they tore down my engine the service manager said and I quote, "There is no evidence of any neglect of maintenance on your vehicle. There isn't even a drop of sludge."
I will most certainly push back on them for this, especially with the information I've learned here!