If a user is restricted by #_GROUP_DIMENSION_DATA_* to a specific area he will usually get a #VALUE error for everything else (in Web as well as Excel). Sometimes it would be more beneficial to treat these #VALUE errors as 0s, so that the user experience is the same as if they would have access to all data (hierarchies etc.) but only their data is stored in the cube and everything else is 0.
You might wonder where this comes in handy - imagine a Cost Center Hierarchy of several hundred cost centers that are arranged productwise while peoples responsibilities are probably more geographical or functional.
[see Illustration in txt file]
In this example one person shall be reponsible for the screws but her cost centers are spread accross two sub-trees. She is not allowed to see any of the other cost centers. For this simple case one would come up with a second hierarchy that is functionally organized but for more complex hierarchies where it's closer to random responsibilities it's not a viable option. The only option would be then to use custom hierarchies for individuals. Something you should avoid and get's a nightmare to maintain.
[see Illustration in txt file]
The proposal is to invent an option per cube/dimension to substitute #VALUE with 0 for people with limited rights, so that everything works as normal - including aggregation - but the user can only consume her own values.
[see Illustration in txt file]
This only works combined with Config / hideElements: N. For a perfect user experience one could implement a logic that only shows the highest tree element that includes all allowed elements (which is not necessarily a root element).
Since there is a notable risk of looking on wrong figures there should be an information in "Trace Cell Value" that indicates whether 0-substitution kicked in or not (maybe with additional info on the affected dimension).