I'm really not sure how to phrase this because I understand all sides of this. There are a few things at play here, but I guarantee that poor parenting is not one of them. In a moment of frustration she told you that she's told her son it's not his fault because of seeing another boy do it at school, but the fact is that you said yourself he was hitting a couple of years ago.
The boy has a tendency to hit already. If he sees other children hitting, it may be making an impression on him enough to mimic BUT he would also see this other boy getting in trouble for it too and THAT would make an impression on him.
Boys on the spectrum can be (but are not always) a little more aggressive physically. Children in general on the spectrum are developmentally behind in a lot of ways, so teaching them things like impulse control (hitting, for instance, which is instinctive) takes extra effort and time. My 10 year old daughter is often like having a toddler in many, many ways most especially with her emotions and impulse control. The more emotionally upset or excited she is, the more she can be physically unaware of herself.
It's also important to consider that while people with Autism feel emotions very intensely, very sensitively, it's still very, very difficult for them to imagine what someone else is feeling. They can be hyper-aware of their own personal space and how other people make them feel emotionally and physically, and have this "bubble" of space around them... but that bubble of understanding doesn't expand to other people. Not only can they NOT put themselves in someone else's shoes, they don't usually even understand what that phrase means. It's very likely that all he knows is, "We don't hit people, it hurts them" but he doesn't know what that means. He can't figure out that other people get injured or their feelings get hurt because of his actions. At six years old, that's not uncommon. It's only been in the last year or year and a half that my 10 year old even STARTED figuring this out.
This isn't an excuse, but an explanation so that maybe people can understand a little bit of the process that's going on. This little boy isn't trying to misbehave. The mom really does sound lost. She needs help and maybe you can suggest to her that she sets up an emergency PPT meeting so adjust his IEP and behavior plan. Having a recess aide simply tell him, "don't do that" isn't working, clearly. They have to figure out what's going on and maybe assign him a one-on-one paraprofessional to help him with the more challenging behaviors at school. They might also be able to point Mom in the direction of some support services outside of school.