Now that you mention it… How could they NOT be?

Fifteen hundred years ago in England, the Saxons, Angles and a bunch of other tribes invaded, and their descendants are now completely mixed… It’s a small country. Everybody is related to everybody by now. How much more so for the tiny wizarding population?

A thousand years is a long time. I’m sure that every British wizard alive today is a descendant of all four of the Hogwarts founders.

A name can die out and can be easily traced. But what’s in a name? Salazar’s family survived to produce Tommy, Jr. in the 20th century. We’re not talking about a direct (male only) line, because the current name was “Gaunt.” We’re talking about every blood relative, branching out in every direction. In all that time, not one little line escaped notice? (Not one secret marriage, adoption, love child, kidnap by gypsies, estranged, disowned, forgotten squib...) The odds are too small to even calculate.

I know that Dumbledore claimed to be sure. But there’s no way he could have known something like that with any certainly. Then again, Dumbledore was known for his arrogance. And JKR never pretended to be a math wiz.