I don't see where doubly positive calcium ions are going to help precipitate doubly charged positive copper or triply charged positive iron since these will repel each other. I think Ben's explanation is more likely since adding Cal-Hypo into pool water that is already close to saturated with calcium carbonate will cause both the CH and pH to go up substantially causing calcium carbonate to precipitate. The higher pH will cause the metal ions to form metal oxides-hydroxides so they'd all precipitate together into the filter.

In theory, just raising the pH should precipitate the metal, but perhaps it's normally super-saturated and needs something to help its precipitation, such as calcium carbonate. This is all just an educated guess, however.