I would promptly take care of the customer if you made a mistake. I would NEVER do such and ask the customer to change feedback - honestly, it's feedback you deserved (if you made the mistake). The only time I ever asked a customer to change feedback is when (s)he left a one star, but raved about how great the item was, shipping, etc. I was confident (s)he mistakenly mixed up 1 vs 5 star.
You can professionally respond to the feedback admitting to your mistake and how you rectified it. As a buyer, seeing this means a lot more than falsifying feedback that was deserved.
But again, I've never and will never use changing feedback as leverage to correcting a situation.