PATCO was a more than slightly different kettle of fish. They had a no-strike agreement in their contract, and they were Federal employees. There is/was a law against some classes of this sort of (Gubmint) employee going on strike, but they walked out anyway. This allowed the Gubmint, in the person of Ronnie Raygun to act. Since you so blithely ignore these sorts of details, the RRs are private companies, subject to the RLA, which essentially says "Use the labor agreement". The Pres gets involved only when contract negotiations have reached and impasse after a considerable number of rounds of negotiation between the carriers and the unions. Even then, all he can do is appoint a PEB. This process continues the use of the contact which has been in use, while the PEB studies the situation and makes recommendations, not mandates, but recommendations.