I would expect the correspondence archives posted online by a reputable entity would be reliable, and I've found at least one source that confirms the story:
As Wagner approached his sixtieth year, he dreamed of owning his own theater and stating is own works in ideal circumstances […]. In Zurich, Wagner told friends about his dream of building a revolutionary theatre, staging his Ring cycle in a model performance, and then burning the theater after one performance. That in a nutshell was his dream: create the perfect theater world and then destroy it. Burt after building such a revolutionary new theater for a revolutionary opera, why burn down the theater? This image reflected the suicidal part of his personality - a desire to destroy both himself and his world.
(John Louis DiGaetani, Richard Wagner: New Light on a Musical Life, page 175)
There's an apparent contradiction between this story and Wagner's propensity to grandiose projects. One would think his purpose would be to left a durable legacy, not to destroy it. However, the contradictory personality portrayed here may be a possible explanation.
Another curiously related episode reported by Wagner himself in his autobiography happened during the 1849 Dresden uprising. Amidst the military manouvers,...
Wagner climbed up [...] the Kreuzkirche tower as an observer [...] and spent a night on its top. As morning came, the composer [...] saw the old opera house, where a month earlier he had conducted Beethoven, in flames. [...] The burning opera house convinced Wagner that "strategic purposes" would "always predominate in the world over aesthetic consideration." (It was an ugly building anyway, he remarked).
(Thomas S. Grey (editor), The Cambridge Companion to Wagner)
Ironically, Wagner himself was afterwards under suspicion of starting the fire, as...
On one of the early days of the revolution Wagner and [the architect] Semper were discussing, in the street [...] the staging of Lohengrin. Wagner complained that the stage of the "new" theater [of which Semper had been architect] was insufficintly deep for his requirements; whereupon Semper, half-angrily, hald-humourosly, replied,"Ah well, I'd like to burn the place down myself!" The conversation was overheard [...] and after that, of course, it only needed the conflagration at the "old" opera house for the crime to be fixed on Wagner and Semper!
(Ernest Newman, The Life of Richard Wagner, page 78)
So the idea of destruction by fire to allow renovation is one that could have been in Wagner's mind for many years, at least metaphorically.