To be clear, you DO need a starting DBR that establishes your start time. Same for ending DBR. The good news is that almost any computer generated DBR will do as long as it meets the definition of 'DBR'. Hotel receipts, 7-11, ATM, local diner...etc.
Best example I can come up with: The Cape to Cape ride, Hatteras to Cape Medocino. East to West you would ride to Cape Mendocino, Take some pics, mark a point through Spotwalla, and then ride back 20 or 30 miles to the nearest town and get your official ending DBR. The clock would not stop until then. Same issue in reverse if you went West to East.