It's even more remote than that. It's more like Norwegians claiming that they used to rule Britain because Vikings had, at one time, a foothold in what eventually became Britain. There was nothing even remotely resembling a single country called China in 3,000 BC and 'northern China' could easily be thought of as Mongol territory (depending upon how 'northern' we're talking about) assuming there was anything resembling a pre-Mongolian culture that far back.
It seems pretty clear here that within the scope of what China calls its history life (6000 years), Northern Chinese didn’t just “get a foothold” in Tibet, they outnumbered any previous inhabitants.
Now when China effectively relinquished Tibet (so much is not said about the independence years, but I assume China just didn’t want to bother), should that count for good? Being a native of a young country I would say yes by the standards I know, but it’s probably more kind of like how China thinks of Taiwan.