Yes. Actual real people believe that LLMs are actual, thinking, intelligences, perhaps even with consciousness.
Your bit with MySQL is harmless because it's obvious that a database isn't a sentient lifeform. But LLMs can look like they're the real deal, and people believe it is. Using terminology like "thinking" and "reasoning" to describe what they do only reinforces this.
Having said that, I agree with you on the terminology front: I'm not going to say "learned prompt augmentation tokens" either.