"Ginnie said she had discovered that 'a woman I know and work with, a fellow teacher,' was having an affair with one of her students."

So, was the woman having an affair with one of her own students, or one of Ginnie's? It was perfectly clear to the writer, of course—and that's part of the problem. It's too easy for the writer to overlook the fact that the reader doesn't know what the writer knows. When writing, you have to put yourself behind the eyes of the reader, and read with the reader's limited knowledge.

If you want to decide who's having an affair, and then revise the sentence to make it clear, feel free—it's good practice. And feel free to let us see your revision.