Private Browsing has no connection to trojans, etc. It's certainly a bug if Private Browsing is on and it's still recording your web history, but that history is only on your computer. It also doesn't save the pages themselves, but only the web addresses (so no contents of your email), with the exception of the thumbnails that are generated for the visual history search. I understand not liking that, there's talk about how to disable it, but saving your history is not putting you at any risk of viruses, trojans, etc. 100% unrelated things.
jW