Could be, maybe even probable. And maybe they figured it out too, but decided to stick to their story of the headless man because, well that's more interesting innit?

And one more thing, this was in the days when capital punishment was still in effect, but with a growing opposition from the humanitarian, enlightened liberal bourgeoisie. And a story about how a decapitated criminal is haunting arbitrary pedestrians does fit that agenda. All subconsciously construed of course.