Is the Neanderthal Theory of Autistic brain a reasonable scientific theory? I've recently learned about The Neanderthal Theory, that explains autistic (and especially Asperger's) brain functioning as the effect of genetical similarity with Neanderthals. 

The author gives a great number of examples of differences between modern and Neanderthal human, that in the same fact are strongly correlated to differences between neurotypical and autistic brain. Most of them greatly applies to me, which biases me towards accepting that theory:


Neanderthals have less developed social life, so their social skills were less developed too, so are the social skills of autistic people
most primates avoid eye contact as the sign of aggression, modern humans (neurotypicals) are the exception, both Neanderthals and autists are not
Neanderthals have bigger brains, and the proportion of brain size to body size was bigger, that could mean they were more intelligent, people with Asperger Syndrom are typically more intelligent than neurotypicals
by Neanderthals women were dominating and were taking sexual initiative, autistic people find it especially difficult to adapt to sexual model of neurotypicals, where males are sexually dominant, increased tendency to behaviours such as exhibitiosm can also be explained by neanderthal genes, since among Neanderthals such behaviours were actually accepted as normal and dominant
Neanderthals were meat-eaters (for me meat is the best diet)
Neanderthals prefer cold to heat (I like when it's cold and hate when it's hot)


This all makes sense, however, I'm aware, that it's quite easy to find a theory that will exactly match the known facts, so each theory must be proven by new facts and experiments. So I ask for any facts and scientific articles that would either support or reject that theory.
I don't know if it's a reasonable scientific theory, but here's some more info:

Autism: The Eusocial Hominid Hypothesis

ASDs (autism spectrum disorders) are hypothesized as one of many adaptive human cognitive variations that have been maintained in modern populations via multiple genetic and epigenetic mechanisms. Introgression from "archaic" hominids (adapted for less demanding social environments) is conjectured as the source of initial intraspecific heterogeneity because strict inclusive fitness does not adequately model the evolution of distinct, copy-number sensitive phenotypes within a freely reproducing population.

Evidence is given of divergent encephalization and brain organization in the Neanderthal (including a ~1520 cc cranial capacity, larger than that of modern humans) to explain the origin of the autism subgroup characterized by abnormal brain growth.

Autism and immune dysfunction are frequently comorbid. This supports an admixture model in light of the recent discovery that MHC alleles (genes linked to immune function, mate selection, neuronal "pruning," etc.) found in most modern human populations come from "archaic" hominids.

Mitochondrial dysfunction, differential fetal androgen exposure, lung abnormalities, and hypomethylation/CNV due to hybridization are also presented as evidence.

A short video introduction