John Hawks on the FoxP2 in Neandertals

John Hawks came up with a FAQ on the recent finding that Neandertals (or at least the two they got DNA from) had the same version of FoxP2 as us.
He raises some interesting points. First is this the best strategy vis-a-vis getting the most info out of a precious DNA resource. What other genes would be interesting to look at?
The FAQ goes on to questions about what we know about the role of FoxP2 in language, what we know about whether Neanderthals were capable of speech.
Then..., I like this question:

We all know that the Neandertal genome is riddled with contamination from modern humans. Isn't the null hypothesis that we have a modern human sequence here because it is a modern human?

According to John, we shouldn't worry too much:

For this study, Krause et al. (2007) developed a test of nuclear DNA contamination: they identified seven gene variants that differ between the recovered Vindija Vi 33.16 nuclear genome and all known living humans. In other words, these are human-derived mutations that are absent from the only known Neandertal nuclear genome. Then, they probed the El Sidrón bones for these sites. They found only the ancestral form in their extracts of both bones -- presumably because no human contaminants were present in their samples.

he then goes on to discuss vasious timing issues. I started getting lost at this point. He does this in the context of the possibility of this being an example of introgression: i.e. the Neandertals got this version of FoxP2 via mating with humans. I guess you could picture a really talkative "modern human" female mating with a grunting Neandertal male. Or it could be a case of introgression the other way around (Neadertals into moderns):

So, considering that the El Sidrón samples both share the human-derived amino acid substitutions on the same haplotype as modern humans, complete with all the high-frequency derived SNPs, it seems almost certain that the gene introgressed into Neandertals from modern humans.

Or, there's one other option. One of the El Sidrón bones includes a relatively rare (in humans) ancestral SNP allele at one of those linked sites where the derived allele is at very high frequency in humans. One explanation: the selected mutation arose in Neandertals and introgressed into other humans. That would explain why this Neandertal didn't have a SNP variant on its FoxP2 haplotype that later became very common in humans: Neandertals had the new FoxP2 first.

I had a hard time following the reasoning throughout his post (mainly due to my unfamiliarity with all the intricacies, and due to time limitations), but thanks, John, for breaking it down so thoroughly for us.