@ merlak
Thanks for the clarification. Clearly, you're right: the counter doesn't show how many messages are displayed, but how many filtered are active / inactive.
@ MakimKi
It was at the beginning of a game. And the problem wasn't that it showed only one message per say, it was that I interpreted the UI as meaning that 68 of 68 messages were shown. But, thanks to merlak, I now understand that the counter has nothing to do with the message count but instead with the active / inactive filters.
There is something weird going on though. Here's a screenshot of a later point in the game, where I've set the filters so no message should be displayed. Yet, there are plenty of messages still displayed.

- Messages still showing.png (305.18 KiB) Viewed 20 times
So plenty of messages are shown even if they're all supposed to be filtered out.
Also, the title bar of the message log indicates "Showing All Messages" (presumably because that's the notification panel section that is active). I think it would be more useful, if, on that title bar, a counter would instead show how many messages are actually shown in the message log (that could help in identifying problems with notifications and filters).
I've attached the save in case you need it: