I guess it depends on where the "third world" stops being third world (beyond the original definition of "any nation that isn't aligned with either NATO or URSS"). If third world is used as "developing nations", not every country that would fall under that label is necessarily a failed state. Not all Latin American countries are Venezuela, and not every county in California is San Mateo. In LA and SF I've seen huge amount of people in homeless encampments, to the point where family from Latin America pointed it out, and where European family and friends were completely horrified.
I completely understand your point, and a rich person in the US is in a better situation than in other countries, but I wouldn't say that the poorest among the population US are _that_ much better than in other countries. My guess is that the people pushing for the view "parts of US == third world country" might be looking at the top of the list for those countries, while you and others that seem against this comparison are looking at either the average or lower half of countries considered third world.
I personally found it horrifying to see a Lamborghini waiting for the traffic light to change while a legless homeless veteran coughing up blood was on that intersection asking for food. Worst part of it though, is that once you live in that environment, very quickly it fades in the background and turns into "just the way things are". Poor people in this country have access to more goods than poor people in other countries, that's true, that doesn't mean that services are up to the task for them.
