Neanderthals and Language Gene

Did Neanderthals Share the "Language Gene" with Homo Sapiens? A Galaxy Classic: Interesting and thoughtful article regarding Neanderthals and language. The inter-breeding theory I believe is valid. It seems quite likely that some Neanderthal blood courses through all of our veins. However, I'd like to present the possiblility that the FOXP2 gene, which is obviously shared between Neanderthals and modern humans could exist in both thanks to Homo Erectus. Why is that possibility not discussed? If Homo Floresiensis (Hobbit) were scaled down Homo Erectus' and tool makers..... why not talkers as well?