You're getting ready to sue somebody for what? If you ran over a skunk and couldn't get the smell off the car would you go sue somebody? Do you have some strange idea that purchasing an extended warranty is some right to having a perfect car that is always exactly in order according to your own perceptions? I guess, in other words, what are you talking about?
As for the problem - I can't think of a single thing about a car that is going to give you a natural gas smell unless you happen to have a car that was converted to run on natural gas. There is especially nothing that has anything to do with a blown and new tire that would smell like natural gas.
Did someone at the dealership drive the car? Did they smell the smell? What did they think about it? Are you sure you know what natural gas smells like (b/c it actually smells like nothing - the odor is added so you can tell if it leaks)? Or are you smelling gasoline fumes? That would make sense.
Or are you smelling something like sulphur (which, I believe, is normally what is added to natural gas to give it its warning odor). If you are smelling sulphur, try a different gas station for a while. Some sulphur goes into some gasoline additives. Different stations may have more or less of certain types. While you're at it make sure that all recommended maintenance is up to date on the car.