Hi Tony,
I took sample data and ensured that an AR customer had bills retrieved and posted from Time&Billing. I then created a Cash entry to pay everything for that customer, leaving the balance at 0.00. When I printed either the Overdue Receivables or Aged Trial Balance reports as of today and excluded zero balance customers, this customer correctly did not appear on the report.
So it should work. But if it doesn't for you then there is something missing in the information provided. For example, are you backdating a report earlier than the payment date for the customer or vendor? Some reports will recalculate transactions as of the report date. What are the AR/AP/TB program versions? What current (unpurged) transactions exist for the customers/vendors? What are the report date and other options? And so forth.
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Regards,
Softrak Tech Support