Along with the airline obviously having a larger plane available to fly (not due to Tina's persuasion) was that of course that airline will switch to a bigger plane if they can. The other flight was on a different airline. If they hadn't switched to the bigger plane they would have lost all that money. It was only a fiscally sound move for them to switch.
And why does Tina think the other teams should thank her? Big deal, they all got on that earlier flight. There were not enough seats on the other one and they all would have taken the later flight. They still would have all been together. Even if she really was responsible for the airline switching the plane what did that gain them except less time at the airport. They were still all bunched together and had the same opportunity getting off the plane at the earlier time as they would have at the later time!