Is it ever legal in the USA not to have two brakes on a bike?
Many places have adopted the Uniform Vehicle Code language.  It currently states:
 12-706. Brake required Every bicycle shall be equipped with a brake or brakes which will enable its driver to stop the bicycle within 25 feet from a speed of 10 miles per hour on dry, level, clean pavement. (FORMER 11-1207(c)).
The goal of the UVC is to have consistent laws between states, counties, and municipalities.  It doesn't entirely work - often the process of changing the laws is too complicated, so many outdated variations exist.

In 2006, Portland, Oregon saw an interesting challenge a similarly-worded law.  A cyclist was cited for failure to have two brakes, even though the fixed gear on their bicycle allowed them to meet the requirements of the statute.  (Ridiculously, the previous UVC phrasing that the ORS statute is based on doesn't even require the ability to stop, only the ability to skid.)  The judge and ticketing officer's contention was that a brake must be a separate device.

Meeting the UVC phrasing is your best bet for a US-wide policy, but definitely review the local statutes for the places you will be riding if you are concerned.