For Web Store-generated Sales Orders, when both Credit Card and Terms is tried to be set on the Sales Order during creation (e.g. through user event scripts), the back end logic checks whether if a Terms value is being set and applied. If found, the Authorization Process is skipped.
Terms being prioritized over Credit Card is only applicable during creation of the sales order from the web store and in the context of Authorization Process.
Solution
Hence, one possible reason why the Authorization process is skipped for credit card-based sales order event when the Web Site Set Up preference Require Authorization for Credit Card Transactions is enabled, it is possible that a customization is setting the Terms field on the sales order.