The term "dependency injection" comes off as very showy to me.

People who are poor communicators take pride in using terms like "dependency injection" when, as you point out, they could just say "we'll create/encapsulate it here and pass it in as a method parameter here, so we can share the instance and/or specify the concrete type at runtime" or whatever description is relevant to the specific situation.

It's like creating a vague term to save a few words when referring to it but at the cost of having to expend thousands more later trying to explain it later, but with the benefit that the users of the term look like they know some special technique other people don't.