Does the Payables Open Interface Import run across multiple orgs?

Our client has a number of Operating Units, each with their own org_id.  They receive invoices via the xml gateway and these are placed on the Invoice interface tables, to be picked up by the Payables Open Interface Import request.  Our client has a number of suppliers who are common across each of the orgs.  The suppliers are set up within the xml gateway trading partners, but only one org has the Invoice inbound processing details configure.  When the request is run for org A, it picks up all the invoices in the interface and tries to process them, even