You're missing a big aspect of it: what about the ownership corporations have over society? That has nothing to do with "dumb rednecks", and it's certainly not subtle. From Carl's Jr. taking custody of a woman's children, many people named after brands, the diatribe on Brawndo owning the FCC and FDA, the Costco law school, language ("Listen, I supersize with you but you broke the law"), etc.

I thought the main point of the movie was that people's intelligence deteriorated past the point to recognize that they had lost their agency. Mocking lowbrow culture was an aspect of the satire, but I didn't see it as the main point.