I just got done this evening amending a 3' x 20' bed that had a lot of clay and some composted cow manure with about 4 cubic yards of the dry peat moss. I tilled it in very good and found it breaks up the clay quite well with deep enough tilling.
After reading this i will certainly get the bed very wet and i water the plants in the hole before and after back filling.
I have never had a problem such as described with dry peat moss but if it was simply laid on top of clay without being mixed in very well i could see where a thick enough layer could act as a water barrier. But it sounds like you got the kind that is more black dirt looking than dry. Never had that problem either as i have used that too.
I also take care to water under eves where plants may not get all the rainfall as others do out in the open. We also have nothing but clay here and yes sand does not help break up clay like dry peat does.
Don't know what you were sold but i hope you get it figured out.