I don't think parents need to have access to bedrooms regardless if their child naps there.

This isn't a daycare center (as playfelt stated), this is a private home that provides childcare and rules are different. And yes these bedrooms can be thought of as private even if their child uses them for a 2 hour nap.

I use all 4 of my bedrooms and parents like it that each child has their own room. I'm fortunate that all my parents respect the fact that this is still my home and that although their child is here, I'm entitled to boundaries. No parent is allowed to wander throughout my house. They can enter the mainfloor play area where children spend 80% of their time and that's it.

You are most definitely able to maintain privacy in your home while running a daycare, I've done it.