HOW LEGENDS ARE DEBUNKED.  The register of visitors included at least one individual seeking enlightenment about President Roosevelt's train mysteriously abandoned and forgotten under Grand Central Terminal.  It's not yet a topic worthy of Snopes, but we can refer to that story as a myth.  With a correction.

A closer inspection of the picture suggests a New York Central baggage car that got pushed out of the way under the Waldorf-Astoria and subsequently proved to be too expensive to haul away for scrap.

It was a steam-era baggage car, but not New York Central.  This site, which makes reference to that "mysterious bulletproof freight car," has two pictures of it.  Look closely at the uppermost picture, and read down.

The baggage car ( "bulletproof freight car") was left by Penn Central for worktrain service and the MNCX reporting mark was painted on the car in 1984 in North White Plains shops (not by the Secret Service).

Left by Penn Central, and subsequently moved to North White Plains for painting.  But Penn Central didn't get it from the Roosevelt estate.  THE Magazine of Railroading has a forum all about the armored freight car that isn't.  It's a Pennsylvania Railroad car, and there's no way The New York Central System is going to be assigning a Pennsylvania Railroad baggage car to President Roosevelt's train.  But Altoona built 'em to last, and two of them cascaded to wire train service on the lines out of Grand Central Terminal.

As far as the other secret stuff supposedly under Grand Central, well, look carefully at the diagrams in this feature on abandoned stations in New York City.