I have found the answer to my question.
The AllPermissions propety is displaying the permissions for the linked table in the frontend (which has default security, ie users group has all permissions on the object). It does not see the permissions of the table in the linked db. I had to create a database obect of the backend and query for the permissions on the table there.
Please forgive me, but I am display code from both the module and the immediate pane here:
Dim dbBackEnd As Database
?currentdb.TableDefs(me.RecordSource).Connect
;DATABASE=V:\PathToMyDatabase\MyBackend.mdb
set dbBackEnd = OpenDatabase("V:\PathToMyDatabase\MyBackend.mdb")
?dbBackEnd.Containers("tables").Documents(Me.RecordSource).AllPermissions and dbSecRetrieveData
20
?dbBackEnd.Containers("tables").Documents(Me.RecordSource).AllPermissions and dbSecInsertData
0