It is not so much about me being important, it is more about me guarding privacy/autonomy/independence. It is not about your worth either, usually it is about that person negotiation tactic. Even if it would be laziness (or need for rest), you are still asking some extra time I don't ow you from me.

If saying the reason would not lead to people taking advantage of it, I would say it. But with many people it does.

But I would not just brush you off, actually. I would attempt to find a way to help you if I would see one or attempted to redirect you to someone who can help. So even if I wont do what you want, unless I have bad experience with you personally, I would try to figure out alternative solution.