IME it's often used as a sort of sarcastic parody, to emphasise that the element of the person's statement being questioned hasn't been resolved and the whole situation is contingent on the answer.
For example, when PM May had finished presenting her new manifesto before the election one might ask "Quick question: how are you going to pay for all that?" to highlight the fact that no costings had been included and suggest you thought it was unrealistic (or hiding tax rises, or whatever).
"Quick question" is used genuinely too. One use appears to be "don't go too deep, give me a superficial answer".
