The Ledger List of Values on the Run Financial Reports form shows all possible ledgers. How can this be limited to only ledgers the responsibility should access?
The Data Access Set assigned to the Responsibility (via the profile GL: Data Access Set) controls which ledgers you can actually update or view data for. Even if there is a ledger name in a LOV, you should not be able to see the data for that ledger in the FSG if the Data Access Set does not have that access.