Everything about the old story of the idea to arm a large quantity of bats with incendiary explosives, to attack a fire-prone city reads like information that might be fed to suspected moles in a counterintelligence operation.

The idea being that you wouldn't knowingly jeopardize real plans, by gambling their exposure among an untrustworthy audience, but, since counterintelligence is an understood expense, allocate some funds for seemingly outrageous boondoggles, and see if those secrets circulate.

  The bat bomb plan was stamped “top secret” and 
  assigned the suitably sci-fi code name Project 
  X-Ray.

Figure there were three types of people that were granted access to the classified information, while it was still classified: those hunting for moles, suspected moles, and authorized individuals kept unaware of the mole hunt, but confirmed as definite non-moles. Assume FDR was probably clued in on the nature of the exercise.

Why take it so far? Probably victimization by sunk cost fallacy, plus persistent suspicion and paranoia. Plus, when the time came to retire the project, it might have gained some extra inertia all its own.