HFM security restrictions at base member vs. parent (custome 2 dimension)

Hi. We are experiencing a security issue and wanted to have a better understanding how how security should work in HFM.

If a group in HFM has access to a base level member of a custome 2 dimension but "none" access to the parents above the base member, will they be restricted from viewing any data in HFM? That appears to be the case when we try to allow access to a base product in our product dimension but when removing the access to "Total Product" member on the higherarchy, the group loses all ability to view any data.

Appreciate your feedback.