There is no flat tire rule that puts guests on a different airline, why would the airline pay another company to fly you when you were late? One time I showed up for a flight, 6 first class tickets to Hawaii 1.5 before the flight. We (my fault) went to EWR when our flights were actually out of JFK. What a nightmare. Delta could have charged me thousands... But instead they found us 6 first class tickets out of EWR for no charge. Flat tire rule? Idk. Point is it is always their discretion