It's possible to have those on two spectrums; the Autism one and the ASPD umbrella.
Look at Adam Lanza's case; sounds psychopathic.
Most Autistic feel empathy, they may not always show it.
However there stands to reason some Autistic ones may suffer from psychopathy or another disorder under the AntiSocialPersonality Umbrella.
Of course the controversy would piss off a lot of parents of Autistic children who don't have a mean bone in their body. Likely why the media didn't dive into Lanza's Autistic Diagnosis too much and when they did they had kid gloves on.