This gets asked every once in a while. Here's the most recent about Confucius in a thread about oldest known lineages.

There are other times it's been asked, or a more general question about oldest lineages have been asked, but that's one of the better recent ones.

Generally it's accepted that the lineage is verified. There is a long and strong tradition of accurate records of family descent in China, though obviously they've been falsified before. There's not any particular strong reason to doubt that his so-called living are descendants of Confucius as they claim.