I think I might have got it.
The teller says, 'There once was a man called Boswell. For short they called him Bos, and he walked up the post office steps.'
The listener, in their confusion at the nonsensical riddle, asks, "Well?" (Meaning, so? Is that it?)
The teller says, "I really can't tell you?" (Meaning...I can't tell you if Bos walked up the PO steps 'well' (ie properly) or not, because I don't know)
It is a play on the word 'Well'. The listener asks 'Well?' meaning 'Tell me more." The teller takes this to mean 'Did he do it well?' and so answers "I can't tell you." (Because they don't know if he walked well or not).
That is why the answer will always be 'I can't tell you." because they really don't know how well he climbed the steps.
This has got to be it, surely? If this IS IT, it is SHIT!