Are you sure Dawkins wasn't saying that there isn't AUTOMATICALLY a connection?

Yes. He says that there is a logical path to atrocities for Christians but not for Atheists. And to make that more convenient, he says that Maoism and Stalinism were religions. Apparently his test of whether or not a belief is a religion is whether or not it can lead to atrocities.

Dawkins' form of Atheism is as dogmatic and fantasy prone as any other religion.