I don't know for sure but just a thought here.Not saying anything here about legality or illegality and all but confusion over refiners accepting, or not accepting Copper, Silver or Gold Coins might not involve them melting them down.
It seems there are conflicting experiences here. Some say that refiners will accept SILVER coins and others say they will not take US Coinage. The confusion may be in how a question is asked and then answered.
I would doubt that any refiner would accept common or clad coins, (Modern day Nickels, Dimes Quarters Pennies and Halves.... SBA and SAC dollars and so on).Nor woud they probably accept pennies, unless they are high percentage copper. Reason being is that there is little to be gained from it as the cost of refining, especially the pennies, as explained would be more costly than their value. Some might be willing to accept the older coins that do contain large amounts of copper, silver or coins that contain gold but, probably to resell and trade rather than melt down. Reason for this is that refiners are also in the business in investment in precious metals. They may buy all kinds of scrap or unwanted items like old jewelry and such. That doesn't mean that they melt it all down though. If they found a really unique Silver Candle Stick or Gold Ring, it might be possible that they have ways of selling such items to other types of dealers or sellers, Auction houses etc. What they don't melt down and sell to other manufacturers etc., they might be able to trade, in countless ways based on the metal content or other values.
I remember talking to a refiner one time who would take my scrap Gold, Silver and other metals and give cash or Bullion Coins of my choosing. They are modern new coins available in Gold, Platinum and Silver and he had a large catalog to choose from. China, Australia, South Africa, Canada, US etc. Perhaps refiners that offer these services to their clients will accept the coins and hold them, or trade them on their metal content to acquire other coins. Like me selling one form of gold, (dental scrap for example) and getting another in return, (Bullion Coins). In the middle, the refiner takes his percentage off the top and then returns the ballance in coins. He then takes the metal I gave him and either refines it into it's raw materials and forms it into ingots etc for sale to manufacters or he may keep it and hold it until he finds someone who wants a specific item or maybe until the spot price rises to a point where he can justify re-selling it or processing it.
I don't know about the older Quarters, Dimes, Halves and Dollars and how closely their prices may fluctuate with the spot prices for metals but I do know that the Bullion Coins do fluctuate. They contain several values. Face, Metal Content (Spot) based on their weigth and then, Numismatic value.
So, some refiners might accept the better coins on the basis of them getting a return on their spot value or Numismatic value by reselling them rather than melting them. Just another aspect of their business of investing in precious metals.