The DNA analysis not only backs up the evidence, but it's is a different kind of evidence. Language or pottery styles could theoretically be transmitted without there being a trace in people's genomes. Memes vs genes if you will.
With people walking a few hours between villages, ideas could theoretically spread at >10 kilometers a day. At 100 walking days a year, that's Rome to Paris in a year, easily. In practice, transmission speed would be way lower, but given a few millennia, a lot is possible.
And, by the way, that applies to genes, too. There is no need for statistical east-west drift of humans for genes to spread from Asia to Europe. All you need is (way) more people in Asia than in Europe, and people moving a few km in random directions between birth and adulthood (oceans limiting such movements would help, too, but aren't even necessary)
You needed a lot more than a few hours to walk between the villages in the Eurasian steppes, mostly because there were no villages there.
Population density back then wasn't what it is now.
http://arheologija.ff.uni-lj.si/documenta/pdf30/30richards.p...