Diagnosing Others

My uncle (moms brother), Ill call him J has autism. Or at least thats what I was told my whole life.

The other day I asked my mom when J was diagnosied with autism and she said he wasnt actually ever diagnosed. Aparently when he was a toddler, my Nana and Papa took him for an autism assessment and they said J had learning difficulties but wasnt autistic. But my grandparents decided that the doctors were wrong and say that J has autism.

Is that allowed? I know you can self diagnos but I didnt think you were able to say that someone else is autistic.

J is in his 30s and still lives with his parents. He used to have a job at a grocery store where all day he would take in the shopping carts from outside to inside (they moved though so he needs a new job). He really likes bears because there is a book with a bear who has the same name as him. He watches cartoons. He likes to put his face in their dogs fur (sensory?). He spends time alone but he also will be with everyone else but he kind of only talks about his own things. J also does this thing where if he wants ice cream then he says "There is ice cream in the freezer" then Nana will say "Do you want some?" "No no thats okay. I dont want any, I just was saying there is ice cream in the freezer." "You can have some if you want some." "Okay Ill have some." I havnt noticed that he has any repetitive or restrictive behaviors though. 

I think he could be autistic, and I dont mind thinking him of being autistic. But do you think if was okay for my grandparents to say he had autism? He didnt self diagnose but at the same time I guess if the doctors made a mistake then perhaps it would be okay?