If the "busy person" is so rude that they wouldn't want the introduction in the first place, then they can be that rude themselves

I disagree. The "busy person" didn't ask to be put on the spot to decide whether the inviter's social capital is insufficient to overcome their busy-ness or lack of interest in the intro or whatever reason they have for declining, so you shouldn't put them in that spot.

Assuming it's laziness totally misses the social dynamics.