Thank You Norman for this suggestion.
I was also thinking about the same, but there is one problem - we use "simplified access control" and therefore the "filter" option is disabled in my case.
We use this option as we were experiencing significant performance issues in past (and still are in some cases, like recalcuation of MX_ASSIGNMENT attribute) and I am very cautious about using functions which SAP claims as "degrading performance" as those are often the first ones they ask to disable, when I report a performance issue 
I will consider turning this off though, if there is no other solution found. I assume that turning it off itself does not degrade performance. It's rather the way You build Your filters that determines if the performance of task access determination is degraded or not.
Once again - thank You for suggestion. I am still wondering why the "out of the box" solution does not work and should it work at all.
Darek.