A train seat is not the thing I am paying for. A transit company is typically chartered around provision of service regions and schedules, and it has the power to divert passengers to alternatives like buses if problems arise preventing use of some existing infrastructure. The customer is not there to "ride the train" but to reach a destination - the transit is judged upon how well this demand is satisfied.

Private property law allows owners to enforce their own rules(to a point). This both explains the private control over the train and tracks and lends weight to the possibility of being kicked off the train, as it is justified in terms of disruption to service and resulting monetary losses. To wit, a positive externality of transit service is economic gain from the population having improved market access(more goods, services, workplaces within reach). The transit company does not realize these gains, the public does. The company's enforcement of rules is guided by the premise that some amount of security and order is necessary to achieve its service goals.