Let me try to explain again. AINP does not participate in the Express Entry simply means they do not go through the Express Entry to invite or nominate candidates. However, once you get an AINP nomination, you have to go through the Express Entry program to use that Provincial nomination to apply to the Government of Canada. To do this, you will create your EE profile. While creating EE profile, CIC will ask you if you have a Provincial nomination and your answer will be YES, so you will get 600 points for that, meaning your total points will then be high enough to get an ITA in the next draw. Only after you receive your ITA can you then submit your Permanent Residency application.
You cannot become a permanent residence with just a Provincial nomination. You still have to apply for PR status to the Government of Canada and that is done through the Express Entry.
I disagree with you