The practice is not to mulch peonies since most over do it and place mulch next to and over the buds. From practice in my area I place mulch on newly planted peonies to prevent heaving before the roots are established in the surounding dirt, animals from digging up plants, so you know where you planted it, especially important if you are filling in an area, and starting to be most important this year is to conserve moisture year around. If you noticed I mentioned removing the mulch from the bud area. In established plants to conserve moisture the mulch should not touch the peony stems and be at least 6 inches away from them.
Mulch in a rainy season if next to the plant crown area can cause rot and promote fungi. Not having any significant rain can kill as can the fungi. I do not think watering and wasting the water by runoff is better than using mulch and conserving what moisture is available.
