In this case, they could cut him off from accessing their data. Out of date train schedules would mean his app wouldn't be worthwhile. But suppose the data was not time sensitive -- imagine if the train schedules never changed.
What then? Once he has the data, what can they do? In the U.S., the Feist v. Rural decision stated that you cannot copyright facts[1]. So it's not covered under copyright, and technically he wouldn't be "using" their website anymore.
What happens then, if the author decided to continue using the data that he gathered against their ToS? Would a civil suit be a (realistic) option for the source company?