I have researched this question and this is what I have found. The US code states “Section 331 of Title 18 of the United States code provides criminal penalties for anyone who fraudulently alters, defaces, mutilates impairs, diminishes, falsifies, scales, or lightens any of the coins coined at the Mints of the United States. This statute means that you may be violating the law if you change the appearance of the coin and fraudulently represent it to be other than the altered coin that it is. As a matter of policy, the Mint does not promote coloring, plating or altering U.S. coinage: however, there are no sanctions against such activity absent fraudulent intent.“
The key here is fraudulent. Defacing a coin to represent it as something else is illegal. Companies have been melting US coins for years. Best I can find is that it is not illegal to melt US coins or turn them into rings, etc. If you have any input feel free to let me know.