It is indeed part of a Minifigure Inventory (like all the other Minfigure parts)
and Minifigures are part of the Set Inventory.
If we would add this part to the Set Inventory there will be 1 too many. So this
change request can't be approved.
You can see all regular parts that are already in the Set Inventory (including
the Minifigure Parts) by selecting 'Break Minifigures' when you are viewing
the Inventory: