A theory of the Hindenburg fire that has recently gained popular acceptance proposes that the paint on the outer surface of the airship caused both the fire and its rapid spread. However, application of physical laws and numerical calculations demonstrate that the theory contains egregious errors. Specifically: (1) The proposed ignition source (an electrical spark) does not have sufficient energy to ignite the paint. (2) The spark cannot jump in the direction demanded by the theory. If a spark were to occur, it could jump only in the direction that the author of the theory has shown will not cause a fire. (3) The most obvious flaw in the theory is the burn rate of the paint, which, in the theory, is likened to solid rocket fuel. The composition of the paint is known, and it is not a form of solid rocket fuel. Even if it were, it would, at best, burn about 1,000 times too slowly to account for the rapid spread of the fire. For example, if the Hindenburg were coated with exactly the same solid rocket fuel as that used in the Space Shuttle solid rocket boosters, it would take about 10 hours for the airship to burn from end to end, as compared to the actual time of 34 seconds. The arguments and calculations in this paper show that the proposed incendiary paint theory is without merit.