It seems the question here is more easily answered than I first thought. If the paternity was withheld from the legal father, then only two people need have known until Schwarzenegger told his wife. The false birth certificate would have eased the way for state benefits and the like. And child support could be done informally, in cash. This happens more often than we may think. I have a close friend who found out his biological father at 16. He was kept out of the loop to make him feel less alienated from his siblings. To make matters more complicated, his mother subsequently married his biological father, whom my friend regarded as his step-father for much of his childhood and adolescence. That'll fuck you up if you are not careful.
A reader writes:
My own parents kept the secret of a much older sibling's paternity until they were in their late 80's when the sibling accidentally found a document stating who her real father was. She was then in her 60's.
When my West Pointer father told me that her real father was his commanding officer (this all occurred 20 years before I was born), I went to the Army post where the triangle took place to learn who the biological father was. After I explained my mission, the post historian told me that I was by far not the only Army offspring to seek information about a biological father. My parents never told anyone about this. It was only when my sister became inexplicably abusive to me that my father (both bio and in law) revealed this to me. BTW, though not religious, she was a hard core social conservative, so this new information stuck in her craw. Sixty years that secret festered. So I know it can be done.
The Dish 