As mentioned in the interview, such waivers are up to the station management. I was rebooked onto an earlier flight in DUS after the lounge lady double checked with the DST if it was OK. So if you notice rolling delays and make your case, a LH agent should plead your case to a person authorised to waive rebooking charges. The trick is to ask them to look up the schedule of the aircraft that is supposed to operate your leg. In my case she saw that the aircraft was running 90 mins late and still had 2 legs to fly before arriving in DUS.
