I would also dispute that a black and white transmission
would not look ok if it was a purity problem.

I've been trying to reason this through. The best I can come up with is
this...

Whether purity is good or bad, the electron beams have to land /somewhere/. In
a B&W image, it might not matter much if red winds up on blue, blue on green,
and green on red. The result will be /something/ approximating a shade of
gray.