There are several points I'd like to discuss in your argument, but I'm going to do so by discussing the Texas dilemma directly, because it both sums up my thoughts and is one that I have personal experience of. I lived for a period in the backwoods part of Texas, went to high school in Austin Texas, and may have a fair bit of intimate knowledge concerning what a 'Aggie' is. I will admit I no longer live there, but instead live elsewhere in the continental united states.
Texas, in my opinion, would be one of the worst hit areas in the country. Partly because there is a MAMMAL problem, not just a rat problem, and partly because of the way flight works in actual disaster scenarios.
First off, evidence indicates that every mammal is a potential carrier for the rash. Hunting is prevalent in the central areas of Texas, and even outside of hunting season it continues on near certain towns I could name. That's one vector. Squirrels and Deer are an issue in and around every town and city, due to over hunting of predators back in the early to mid 1900's, and both commonly eat out of human trash.
Second your argument assumes that everyone with guns will simply hunker down and hold out, safe in their own homes. Issue becomes most of Texas is not as 'country' as they like to think they are. Most of the homes are not sustainable in a disaster, and many of them are cheap suburban construction. Food will become an issue quickly since farming is a secondary activity compared to Ranching, mostly cattle (which again, see point 1). Without food or adequate shelter, people will have to search a increasingly contaminated landscape for food. As you pointed out, many of them are armed, and desperate.
Which brings us to the last point about Texas: Too many people are already there. Texas has some great planes and some amazing views, but it's also filled with people. When desperation sets in, you'll have a wave of refugees spreading outward, triggering other refugees and contaminating the state. They are armed, meaning that it will desperate people vs. desperate people. People will turn, but in Texas it'd be troll season all year round. What you have is a giant mess, with few 'good' natural barriers to prevent the infection from spreading.
That is why I think that Texas, and to a certain extend the rest of the states, would not fair as well under this scenario.
I see your point, but I'd put the survival rate a bit higher. I've lived in enough places in America to know that a few of them would shut down it's borders and kill anyone who tried to enter, preventing easy spreading of the disease. Now, rats could be an issue in the major cities, but many of the cities I've been to had little to no rat problems. I'd say that many of the northern regions would be relatively okay, while only a few southern regions would survive. I could see Texas surviving if only because of their insane mentality when it comes to outside threats, which is to cut itself off as completely as possible. I agree with you, though, that our refusal to visit a doctor might work against us, but it could be an advantage, since sick people would be more likely to lock themselves up than rush to the doctor and spread their disease to everyone they met. The safest place in America would probably be Alaska or Hawaii, though, considering how remote they both are.