It could be the soil, it could be the depth it's planted. Has she been pruning the non-blooming one at all? She may be prunning off at the wrong time.
Is she top dressing the plant (adding soil and making in fact deeper than it was)? Side dress peonies only.
Is the clump too large? Does it need to be divided?
I'll watch for more ideas as this is my second year of transplanted peonie sections. I clipped off the 2 blooms that formed last year in hopes that the energy would go directly to the plant.
ETA I found this website - looks like it's full of helpful information. I'm going to recheck my depth tomorrow and remove the layer of mulch I have on top of the plant.
http://www.weekendgardener.net/peren...ony-100810.htm
It says too much nitrogen causes plants to leaf and not flower. use a 10-20-20 fertilizer