My brother was born mentally and physically handicapped. It wasn't clear right away something was wrong, however it did not take long to figure out something was really wrong with him. Once they did, it wasn't long before he was able to get benefits and see specialist, he at first wasn't suppose to live a year but he did and it took that long to give what he has a name, this was back in 1976 though. I do know ever so often my mom has to send something in that states that he is still disabled, but it's not yearly.
Both of my parents were approved first application for disability. My dad because of COPD and heart disease, however he also had a long medical history of being sick and hospitalized, he died in 2007. My mom applied earlier this year after she was diagnosed with terminal cancer last year, she didn't apply sooner because she was on medical leave from work, once she knew she would not be able to go back she applied.
Those are just my families experiences, I have heard stories from other people where it takes years to get approved and only after hiring lawyers and sometimes not even then and yeah I've heard stories of people getting approved where there is nothing wrong with them. I just think it really is kinda a flip of a coin, if there is something clearly medically wrong that keeps you from working then you get it, but if it's not so clear cut you don't. I really don't know though.