Due to specific reasons with QBO, 'Publish to' is the only field that dictates whether an item has been paid or not.
This means that no matter what you choose (paid/not paid) QBO would always ask you to pick a bank account which then should publish to as ‘Cash’, ‘Check’, or ‘Credit card’.
The only way to publish items as not paid is to select 'Publish to' as 'Bill'.
To summarise: if you have an unpaid item publish it to Bill and all paid items publish to the appropriate 'Cash', 'Check' or 'Credit card'. And you can find more information about this process in here.