Lack of Empathy

One thing you'll often find on lists of Asperger's autism symptoms is lack of empathy or caring for others, and I think that's (for lack of better terms) an absolute load of baloney. The harder you look, the more you see things like it: things saying autistic people are incapable of forming emotional attachments, or even love. I'm not sure if I should be outraged or saddened by things like this. There are many reasons why it may seem like someone with autism doesn't care about others, but I've never come across one who really didn't care about others at all.
One reason is the afore-mentioned lack of social skills. My mom tells me that, when I was very young, I was constantly saying things like "Mama, that lady has a ring in her nose. Does she know that she looks silly?" I had no idea that such comments could hurt feelings then. I remember being instructed not to tell people if their house stunk, and I couldn't understand why. If their house stunk, why not tell the truth? These comments wouldn't have offended me, and in my lack of social knowledge, I had no idea they would offend others. This can lead to accidentally hurt feelings and the appearance of a complete lack of caring for others.
A second reason is that they might not know how to show it. If someone is distressed, and autistic person might simply leave them alone. This isn't for lack of caring, but the opposite. The autistic person might have wanted to be left alone in such a situation, so their way of helping is to leave a distressed person alone. I've come across situations where a person is upset and realized that I had no idea at all how to comfort them. Because of this, I probably came across as cold and uncaring.
Lastly, they may be looking at the situation so differently that they can't find any reason to be unhappy. One thing I hear about autistic children living in religious families is a lack of grief at the death of a loved one. In such situations, the child has been informed that the deceased has gone to live in a paradise called heaven. They are not old enough to think about how this will affect the world in any way but the loved one being happy in heaven, and thus find no reason to be upset. Or maybe someone is upset at being insulted. To an aspie, especially children, they may not think being called fat or ugly is anything to be upset about. Again, they cannot understand why the insulted person is unhappy, and make no attempts to console them because of it.
If autistic people were unable to form connections with others or have empathy, then we'd all be sociopaths and likely murderers. The extremely low crime rate among those with Asperger's alone should prove we are capable of empathy.