In most cases DL has been helpful in various situations, though status does probably helps, especially since I assume they can see your "file".

Almost had this happen about 10 years ago as our rental car got totaled less than a mile from the airport. But AVIS was there so quickly and got us to the airport and through the paperwork quickly so that we still made the flight. I do think DL had a backup for us.

There was a time that I was being driven to DTW to catch a flight on Thanksgiving Eve and the Interstate totally shut down. By the time we were able to call they almost yelled at us for not calling earlier. I didn't fly at all at that time and so all they would do is let me buy an expensive FC ticket to fly home Thanksgiving morning. Oh, why didn't I call earlier? This was the early 70s and for some reason nobody had a cell phone with them.