@Vlad I found this thread as I was gonna make an identical feature request, so I'll answer your question. The additional explanation below the Browser History Privacy Mode control label would have told me how it would solve my problem, but the heading itself didn't make me think it was relevant to my issue, so I didn't read it. When I think "Browser history" I think of looking back in time, I think of my opened tabs as existing currently, not historically.
When I think about how browser history is stored, page titles and URLs, it makes sense that having private history would influence page titles, but it isn't an intuitive connection.