We would need to look at the details, and respect the fact that viruses and some bacteria can copy what we call markers too — as well as the thesis that this is simply a riff that the Lord worked into similar species for similar purposes.
“respect the fact that viruses and some bacteria can copy what we call markers too”
That’s true, but I don’t think there’s ever been an example of a virus copying over the amount of genes we’re talking about here. Most studies are reporting for the applicable human populations, they can trace 1-4% of the genome to Neanderthals. There are 20-25,000 coding genes in the human genome, so we are talking between 200 and and 1000 genes. Cases where viruses transfer genes generally involve a single gene or perhaps a handful of genes transferring. One scientist suggested that a mere 100 genes in the human genome were the result of these types of transfers (from all sources, over our entire history), and most scientists rejected that interpretation. So I don’t think we have to speculate very much to imagine what they would think of 200-1000 genes transferring horizontally to us from a single species.
“as well as the thesis that this is simply a riff that the Lord worked into similar species for similar purposes”
That’s more plausible, but it doesn’t account for why the similarities are more prevalent in areas where Neanderthals and humans coexisted. If we apply Occams’ razor, taking into account that key fact, the simplest answer is interbreeding.