Am I the only one not comfortable with how much "git" has become synonymous with "GitHub" in the common collective?
You're technically correct of course, but remember your audience (important pedagogical consideration). These are new grads that think git and github are synonymous. A slightly less technically correct but grokkable explanation is probably a better stepping stone toward arriving at a more correct understanding. You're description is abstract, which is harder to grok for most people than a concrete example. If you want to be more technically correct and therefore launch into a discussion about DAGs you're also not going to teach them anything.
Note: there are always exceptions, and a good teacher adapts to the audience. I'm referring to the very general case, not the exceptional case.