In my opinion, it raises more questions. You may want to get out your chemistry book.
Electroplating occurs when you place a part to be plated at the cathode in a solution that contains ions of the metal you are plating, and use an anode of the metal you are plating. For plating copper on steel, the basic setup is a clean steel cathode (the part to be pated), copper sulfate in the solution to supply Cu++ ions, and a copper anode to provide additional Cu++ ions. Turn on the power and the copper ions are reduced (they gain electrons) and plate onto the steel as metallic copper. Over at the anode, the copper is being oxidized, so Cu++ ions are going into solution.
So, what is going on with Cheryl's clamps? What is the source of copper ions that are plating on the clamp? Is the wiring the source of copper ions? In theory, these wires are part of the cathode, so the wiring is NOT going to be oxidized and is NOT going to dissolve. Furthermore, because the wiring and clamp are both part of the cathode, the wiring cannot dissolve while the copper is plated onto the clamp. The stainless steel anode shouldn't be a source of copper ions. Finally, why wasn't the cast iron piece that was being cleaned plated with the copper?
These observations initially led me to think that the plating on the clamp was being stripped off, revealing a copper strike under the nickel or whatever the finish is. The Dremel test specimen does not convince that is not the case. You could be seeing the steel that the clamp is made of. But, stripping plated nickel off the clamp doesn't make sense if the clamp is only used at the cathode, unless the charger has a problem, which is a possibility. You've got to remember we use (abuse is probably a better word) these charges for a purpose they were not designed for.
Cheryl, here is a test to try. Get a couple of large (big spike type) nails or other pieces of clean, unplated steel. Wash them so there isn't any oil or other protective film on them. Use your plated clamps to hook them up in your cleaning system. Have one wire, clamp, and nail fully submerged. Run it through the cleaning process for a while. For the second experiment, have the other wire and clip completely out of the solution and only the bottom of the nail submerged. Run your system for a while and look at the results. You'll need to run each nail separately for these tests.
Another thing that might be an issue is you connection between the wire and the clamp. It could be that the a poor connection is causing a problem of some sort. I use a Pony clamp and solid 12-gauge wire that is cut out of a piece of Romex. It will carry 30 amps without any problems. I am convinced that 20 amps is enough current for the biggest piece of hollowware I might want to clean. The wire is stripped and double looped around a No. 12 screw that is tightly attached to the clamp. The other end in looped around a piece of 3/8-inch copper tubing and soldered in place. The tube gives me a large piece of copper to clamp the negative clamp of the charger to.
One last thought. I hang the cast iron from this wire, so you could eliminate the "hanging" wires you are using and just use the clamp and wire for the same function. I can hang a No. 12 skillet by the handle of lift tab or a No. 9 DO from the Pony clamp. Never had any problems with this clamp and wire assembly in years of use.