If I read an interesting anecdote in a book (biography) and want to use that story in a documentary movie, could I use it or is it copyright protected?
Only if you take it word by word and don't give credit. If you take it word by word and do give credit it *could* fall under fair use. If you just use the basic premise no one would probably care, especially if it's not extremely unique. It doesn't much matter how far copyright extends (which is pretty subjective) as much as if anyone can definitely tell where it came from. Most anecdotes aren't unique enough.
Short answer is no. The rights are already held and it is "copywritten". Contact the publicist and ask for the subsidiary rights department. You need to get the rights if you want to adapt a book to film.