Preventing a G/L Responsibility from Reversing an Existing Journal

Is there an easy, standard way in R12 G/L to prevent a responsibility from reversing a journal?

We recently created a new G/L responsibility to allow a user to enter journals for a range of natural accounts within the ledger.  We enabled this restriction using a G/L security rule. 

But this user was able to query up an existing journal batch in the ledger and submit a reversal, even though he could not see any journal lines in the batch due to the security rule.  Ideally, we don't want that responsibility to have the ability to reverse such journal batches, even if it means removing the ability to reverse any journal, even ones that they created.