See the previous entry.
So I found out only one of Cliff's sisters calls the process "cleaning", but several people do remove the flesh of the watermelon from the rind and chunk it up, for a very sensible reason: It takes up less room in the refrigerator. Now that makes sense to me.
Thanks to everyone who commented on Facebook, explaining this (to me) peculiar phenomenon. Nobody else calls it "cleaning the watermelon", though.
Oh, and I found out that only one of Cliff's sisters deals with her watermelon this way. I was corrected. The other sister said watermelon doesn't last long enough at their house to bother doing all that work.