As with many other things, Brown is hardly treading new ground in his works. You can find stories about the secret Masonic history of DC going back decades, even centuries. Some aspects are true, since many of the Founders and later American political leaders were Freemasons, as were many of the designers and builders who worked on building the city, so Masonic symbols are found all over the place. Just look at the reverse of the dollar bill.
The street plan itself is more a matter of correlation rather than causation, as modern Freemasonry evolved in the same 18th century Enlightenment environment that influenced the Founders and artists, architects and planners. The use of geometric shapes in designing cities, with grids and traffic circles, etc., imposing rational design on the local environment rather than following nature, was a very Enlightenment viewpoint, and correlated with Masonic symbolism of God as the Geometer of the universe.
Aspects of this actually predate the Enlightenment and reflect the influence of Renaissance thought, especially the Italian and French Renaissance garden. L'Enfant was influenced by the design of Versailles, for example.
