I don't see the connection. I had pneumonia when I was 8, and I've managed all these years.
A book the length of The Godfather can be nuanced in many, many shades of grey. A movie -- even as long as GFI -- cannot be as easily nuanced. Ergo, characters tend to be painted with a much broader brush. If you extrapolate, just a little, it's easy to see how a guy like Fredo -- dutiful and obedient as he was -- would absolutely go WILD the first time he was away from the strict family environment. I mean, come on! Hasn't anyone ever heard of COLLEGE???
There's enough forshadowing in GFI (his seeming loyalty to Moe Green as opposed to Michael) to make everything that happened in GFII entirely plausable.
Was he stupid? Perhaps in some ways. He certainly didn't think through how MUCH his growing disenchantment with Michael's authority would cost him and his family. But in other ways, he wasn't. He saw the handwriting on the wall. He saw that even though Moe slapped him around once in a while, he had a better shot at gaining SOME form of independence and self-respect working for him. The other way -- being put back under Michael's thumb -- the family's preconceived ideas about his intelligence would forever keep him down.
And isn't this exactly what happened?
BTW, of all the characters in the trilogy, Fredo fascinates me the most. I don't know if it's becaues John Cazale did such a wonderful job bringing him to life, or whether it's because I sympathize with misfits.