Thanks for the clarification.
Yes - If you have a password set for the closing date in QuickBooks, the API will still add the bill to Method, however, the bill will not sync to QuickBooks (A conflict will be created to identify that you tried to create a transaction in a closed period).
Based on your respose, it sounds like you have transactions sync'ing over to QuickBooks for closed periods - even though you have the closing date set with a password. This should not be happening.
If this is the case, I will have our team investigate this issue for you.