I think it is better to speak of uniquely Neanderthal genes. Our genome must have been almost identical to the Neanderthal genome, given that interbreeding was

I think it is better to speak of uniquely Neanderthal genes. Our genome must have been almost identical to the Neanderthal genome, given that interbreeding was both possible and that the hybrid offspring remained fertile. So it is likely that many people alive today do indeed have genes from the Neanderthal line, but those genes are either identical to human genes or so close that we cannot distinguish their Neanderthal original from ordinary variations/mutations.