When Aubrie Lee and Peter Saathoff-Harshfield ride Amtrak’s Coast Starlight up the California coast or the Lake Shore Limited along the Great Lakes, they seek out more than just a seat with a view.

Not everyone in the United States is aware of it, but Amtrak, the country's main railway company, is not private. This quasi-public corporation was founded in 1970 and receives state and federal ...