I think we may just have a difference in perspective. I would call a buggy a car because it has wheels and carries passengers. I wouldn't call it an automobile, because that implies an automatic engine, but I would consider it a form of car.

Same with BBS/Internet. Once you have a series of servers interconnected, and have access to them via an ISP, yes. That is a form of early internet. It dates back to something like the 1960s. Going back to NASA and government usage.

So I think we're talking about the same thing with just a difference of perspective and opinion.