Is this native or is a script/workflow changing Sales Order status back to pending fulfillment and then billed again (after editing a line item)?

That should be native. A workflow can't change the Status of a transaction directly. (Sometimes indirectly).

Why would one natively want the status to be reverted to Pending Fulfillment then again set back to Billed once the order has already been billed?

The only time I see that happening is when someone adds a line item to an already Billed Saels order, OR if a line is Closed on a SO then someone un-closes it it will go from Billed to Pending Fulfillment