A thick enough layer of stones conserves moisture and keeps the soil cool.

Many native plants grow naturally in the rock-covered dirt of the desert.

Organic mulch yes. Rocks no.

There is no mulch that is fabulously better than another. I could even say good things about ground up red rubber (but not anytime soon, I'll need time to think). The subject of mulches is far more complex than black and white comparisons can do justice to. Remember that pine bark mulch is as unnatural here as crushed granite mulch, but both can be good in the right spots and bad in the wrong ones.

Stone mulch is easier to maintain for some people, lasts a long time, and doesn't get as hot as you might think. Mulches shade the soil and in turn are shaded by and hidden by plants to a degree. If you want to reduce the concept to an absurd level of simplicity, all a mulch does is protect the surface of the soil from the moving air.

It all really comes down to what YOU see as more appropriate and how which choice fits your gardening methods. So to answer your question: not necessarily.

My back yard is all mulch (and a few paths made of square pavestones).

I probably would have tried rubber mulch by now if I could be sure it wouldn't make it past the weed fabric. I hear it's a huge pain to get out of the ground and chunks can be found for years if its just put over dirt and you decide to remove it.

One reason I like wood mulch better is it provides nutrients as it breaks down. It's pretty easy to keep it looking good by applying a thin layer over the top every few years.

I went with stone because I had concerns about the wood attracting termites or being even more inviting to scorpions.