Good point. I didn't think of that because it is a totally unrelated word. So clearly it would be as odd to put money in the pisesg as it would be to put it in the kitten.
I can't find a reference to your etymology or to any other. Can you say where you got it? It occurs to me it could be related to Gaelic ciste or similar words in many languages that mean a chest and are often used for the sort of box you keep money in.