I've found solution!
If you want to make Jstats sensible on hints to subpages, you must assign JoomlaStatsActivation module to the same position, as main menu is assigned.
My FAQ module is positioned as 'user9', because it needs to be invisible. I make assignment to it in article body using {loadposition user9}.
When I've installed Jstats modules, I've assigned JSActivation to 'user9' position again, because it seems to be invisible too.
It explains, why jstats counter was activated only when visitors opened FAQ page. Now it works fine and registers all pages accessed from main menu, as position of both - 'JoomlaStatsActivate' and 'MainMenu' - modules is 'hornav'.
Sometimes the best way to solve problem is to 'we(r)balize' it

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Saluti per Tutti
Mark