I grow cambessedesii and clussi in a clay ground with just some grit and composted bark that's all.
They almost double of size each year. The one i grew under glass always die from dryness and floral buds avorted.
2 years ago i saw near Samaria several bands of clusii growing in a heavy and sticky grey clay mixed with round limestone rocks 2-3cm covered with pines.
So i guess they don't fear humic soil.
I'm reluctant to grow them in clay, as I do not have the right clay. It should be crumbly and open. I generally use an open mix with Seramis, lava, vermiculite and one of the better turf based commercial potting soils available here in Holland. Non-Mediterranean Paeonies grow well in this mix with almost no rot. I grow Mediterranean peonies under open cover with a few hours sun and do not let them bake in heat.
So far I grew Mediterranean peonies succesfully from seed up to flowering size in the mix describe above. However, when the plants become larger (and in larger pots), problems arise... It could be the water management, as drying out is more slowly in larger pots so adjusting the water amount is more difficult than in smaller pots. I've come to the point that letting the pots dry out completely during summer is not what they like. Buds shrivel. I think Yann is right with that.
Mediterranean paeonies seem to dislike repotting. And the timing of repotting I find tricky. They keep their leaves well into autumn and resume grows as early as December. So finding the right time for repotting is the challenge.
This year I monitored summer moist carefully and kept them very slightly moist (less water than last year when I lost many plants) by pouring some water on the edge of the pot avoiding to water the root directly. They seem to do better than last year; only two plants died from rot. Buds are already present in most of the plants.
I believe growing Med-peonies in pots is not impossible, once one finds the right conditions. Exchanging experiences, even failure, surely helps a lot.
Cheers, Hans