Up to now, my father has not wanted my sister involved in any decisions regarding his health or estate. My sister is trying to go around him by making this request directly to me and says anyone using the POA has a duty to provide copies to anyone relying on my use of it. Is this "duty" the law or more of a ethical/moral issue?
There's your answer: "...anyone using the POA has a duty to provide copies to anyone relying on my use of it."
Unless your sister happens to be a bank or a court of law, you are not required to provide her anything. As others have mentioned, though, if you feel it will make for smoother relations between the two of you in regards to your dad's care, then you need to make that decision yourself.
Anything for a quiet life, though: do you have any particular reason not to give her sight of a copy if she wants one? It's not like there's anything she can do with it, except perhaps set her mind at rest that you are behaving properly.
My mothers DPOA doc did not address the issue but I can feel confident in saying I am sure about what my parents would and wouldn't have wanted shared with my brothers.
If it were me - if the document allows - I would at least make a copy of the POA agreement and give it to sister. It will prove that you have the legal authority to act as you are and might get her off your back for a while. Beyond that - I'd tell her you answer to your father, not her.