The adoption of the Greenwich Meridian as the Prime Meridian was decided by an international conference held in Washington DC in 1884. It was basically the least bad option, because most charts already used Greenwich, and most trade used time based on it.
fyi, you may find something of interest in this FAQ section
This actually predates the American railroad era. Prior to the invention of an accurate and portable timepiece, ship navigators had a very difficult time figuring out where they were one an East-West plane. (Longitude.) John Harrison was a British clock maker who built the first accurate timepiece in the early 1700's that could be carried on ships. With those clocks, a Captain would be able to calculate with a fairly high degree of accuracy how many hours removed they were from Greenwich England when the sun at their current location was at its highest point.
My conclusion is that while the American railroad system may have perfected timekeeping in the United States, the foundation for that timekeeping was laid down by the very ingenious John Harrison.
My source is a very excellent and very easy to read book regarding this called: Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time by Dava Sobel.
Also the Wiki page about John Harrison gives some good information about this as well.