When the Brightline opens in Florida late this summer, it will be the first passenger-rail train of its kind built in the U.S. in a century.

What’s so special about it? Where the money comes from. The high-speed intercity line is privately funded, built and operated. None of the $1.3 billion cost of the first phase of the operation—laying track and building bridges, stations and complete trains—is coming out of taxpayers’ pockets. The only government involvement is that the project has permission to sell tax-exempt bonds to...