In my humble opinion, the original question goes far beyond sex.
Actually, when asking the question I hadn't actually considered honesty regarding sexual issues specifically. One of the first pre-requisites my partner and I established was that any outside relationships would be both emotionally and sexually transparent. i.e. my partner will be intimately aware of the nature of any other relationships I have.
The responses here highlighted that there is definitely a line between being open about my other relationships, and exposing unnecessary personal details.
But in terms of the original question, I actually was wondering about any deep, personal issue. My family has a fairly complicated history, and it's one I don't generally like to discuss openly. I'm glad that my partner knows about my history though, as I think this part of who I am is important to our emotional connection.
I expect that I would also want to share that history with any potential secondary with whom I become emotionally involved. I guess my question is, if I decided to confess something about my personal history, is it reasonable to expect that my secondary won't tell her primary?
Of course this would also work in the other direction. My instinct would probably be to assume that my secondary shares everything with her primary, and that I should consider that telling her means telling both, if deciding to tell her anything.