Haiku 4.5 is a reasoning model, regardless of whatever hallucination you read. Being a hybrid reasoning model means that, depending on the complexity of the question and whether you explicitly enable reasoning (this is "extended thinking" in the API and other interfaces) when making a request to the LLM, it will emit reasoning tokens separately prior to the tokens used in the main response.
I love your theory that there was some mix up on their side because they were lazy and it was just some marketing dude being quirky with the technical language.