I think a minimally modified "steel man" version of the contended statement is that _modern_ Europeans don't have any _European_ ancestry that goes back beyond

I think a minimally modified "steel man" version of the contended statement is that _modern_ Europeans don't have any _European_ ancestry that goes back beyond 40,000 BC. Their ancestry is known further back; it's just not in Europe. A literal reading of the contended statement is that the ancestry trail of Modern Europeans disappears before 40,000 BC (hence the other poster's comments about aliens), implying no trace back to Anatolia 15,000 years ago, or Africa some 300,000 years ago. I think you meant to state that the family trees of modern Europeans aren't known to have any branches _within_Europe_ in 40,000 BC.