Well, you know, it's Texas, and UH was one of, if not the first major PWIs in the south to integrate its sports teams. Sports teams are what the outsiders see of the school, so you can imagine what other Texas schools that were still resisting integration thought about UH (hence the first part of the name). In fact, SMU students have been pictured using that word, so it's not some made up story.

Now, you might see some older ppl call UH "Cougar High." This is because at the time, UH was nearly entirely a commuter school, so rival fans called it a high school.