Point taken, Caiside.

If we accept that we (creatures rendered immortal by the resurrection of Christ) are uniquely identified with the emergence of homo sapiens 200/300 thousand years ago as the fossil record now suggests, then yes our genes sure suggest we interbred with the Neanderthals and Denisovans. 

However, there is, I think, an emerging caveat.  The recent pushing of our emergence back from 200 to 300 thousand years does open the door a crack to the possibility that this might later increase further so we end having acquired those genes before we branched apart.

But yes, as things now stand, you are absolutely right. Thank you for the correction.