Sorry for the late reply, been very busy with work.
If the permissions are greyed out in Mailbox rights then they have indeed been inherrited from a parent.
This could be one of a number of places....
1) The Mailbox Store the user is in
2) The Storage Group the user is in
3) The Exchange server the user is on
4) The Exchange Organisation
5) Above the Exchange Organisation
Numbers 1,2 and 3 can be checked via properties using Exchange System Manager (ESM).
Number 4 can be checked via properties using Exchange System Manager (ESM) only after you have made a reg key changed.
This can be done on the PC / Server you are running ESM on by following this....
1. Start the registry editor (regedit.exe).
2. Navigate to the HKEY_CURRENT_USER\Software\Microsoft\Exchange\EXAdmin subkey.
3. From the Edit menu, select New and click DWORD Value.
4. Enter a name of ShowSecurityPage and press Enter.
5. Double-click the new value and set it to 1. Click OK.
6. Close the registry editor.
Number 5 can only be accessed via ADSIEdit and I'm not going to tell you anything on that as I very much doubt it will have been set here and the damage you could cause here is massive.
On a standard Exchange install you would have certain permissions assigned to the Everyone group at the Exchange Organisation level although this won't include rights such as Full Mailbox access. Any permissions below that level i.e. numbers 1,2 and 3 you could fairly safely remove them.
At the Exchange Organisation level you need to be more careful and make sure you know what the defaults are.
Hope that helps.