Nope, but there is another explanation.
Sorry for horrible bug report, let me improve it.
1. In a forum list, I see an unread forum icon (screenshot).
2. I click THE FORUM ICON.
3. I see "No unread topics" page (screenshot).
4. Though, there is an old topic with a new reply in toe form (screenshot).
So, apparently it's a bug in the module that implements the "action=unread" argument, like in this link:
https://forum.chaosforge.org/index.php?action=unread;board=5.0;childrenOh wait, it's not a bug but a confusing feature. Who cares about "unread topics found since your last visit" if there are new topics that I didn't open on that last visit.
If the "unread" forum icon link led to "unread;all;", that would solve my confusion.