What is the point of your quibbling over definitions? If you were using this framing as a lemma for something interesting, it would be plausible to entertain. But without that I don't really see much point, because it's just as easy to declare things the opposite of your assertion - eg the term "VPN" doesn't apply to an entire corporate network (as it would per your extension argument), rather just the virtual link part of it. Of course asserting this is similarly pointless without some larger point.