First of all, there is no testing for Asperger's, now known as high function autism, per se. Second, if your son is autistic, the school should have picked up on it. I also think that is not easy to be objective when you are looking at checklists for the disorder.
People with HFA do not act normally or speak normally with anyone. The fact that he can discriminate between how to act with kids and how to act with adults tells me that he is not autistic. That is the thing about HFA, they cannot distinguish differences in social behavior and they certainly cannot adapt their own behavior to something they do not realize exists. Also, HFA people have a ton of trouble figuring out what is a lie and what is not.
Actually, this is good news, though you may not realize it. Having autism is a life changing disorder and the expectations for even mild HFA are not very good. I suspect that you boy is actually gifted, rather than autistic. He has many of the traits, including stubbornness and anti-social behavior. He also may just be an introvert and may not feel safe around kids because they are much more unpredictable than adults. He may fear that his own social ability is limited, but this does not make him autistic.
I have some suggestions for you.
1. Go to You Tube and search for HFA or Asperger's. You will find many experts discussing the disorder and also, you will see kids with HFA as well. HFA is almost always very evident and it is not a does he, does he not situation.
2. Go online and look for a gifted checklist and fill it out. You may find he has even more of these traits than HFA traits.
If you get a positive result form the gifted checklist, go to the school and discuss this with the school counselor, who will give you the official school checklist and will also give one to his teacher.
3. His behavior appears to be very controlling and if this gets to be a severe problem, you might hire the services of an Applied Behavior Analyst to do a functional behavior assessment. Your insurance may even cover it. You will get an enormous amount of information, including whether or not he is autistic. If his behaviors are also occurring at school, you may request that a child study team become engaged with your child and they may request the FBA from school district personnel.
You can find autistic traits in anyone who is highly intelligent, but it is not due to autism, it is due to being gifted and unique. My spouse seems mildly autistic, with the traits of focusing solely on the computer and social marketing and search engine optimization. However, he can interact just fine with people, though he does tend to dominate any conversation, if you let him. However, there are none of the physical traits associated with autism, such as clumsiness, stilted speech or lack of eye contact. His IQ is 162.