The request understood accurately gives a refusal a fairer meaning.

A no only means something if the question was heard properly. When someone declines a version of the request you did not make, the answer lands as rejection while actually replying to a different question, and both people leave with the wrong information. Understanding first costs one sentence. It also makes the refusal, when it comes, something you can trust.

Before answering a request, say back what you think is being asked and let the other person correct you. When you decline, name what you understood, so your no is clearly about the real thing.