I'll try to answer with out nerding out too much:
Basically, acids in your water mean you have an excess of hydrogen ions floating around. So, adding peat puts these ions into the water. However, hard water means you've got a lot of stuff like carbonate ions floating around. When you add the acid (from the peat) the hydrogen ions react with the carbonate and come out of solution. Thus, when you've got lots of carbonate present, whatever acid you add to the water is going to just get "used up" by the carbonate and won't help in making your water more acidic (i.e. lowering pH).
However, if you've got soft water, there's nothing there to "use up" the acid you're putting in the tank by using peat. So, if your water is suitably soft, adding peat can effectively lower your pH.