That is a very common misconception.
Rest assured the coin jewelry you see here does not violate any US statutes. These beautiful little pieces of art are created with a purpose, to wear as jewelry, not with the intent to defraud someone. Fraudulent intent is the key.
For example, we are not gold plating one coin and attempting to pass it off as a different, more valuable coin.
U.S. Code is 18 U.S.C. §331 reads: “Whoever fraudulently alters, defaces, mutilates, impairs, diminishes, falsifies, scales or lightens any of the coins coined at the mints of the United States, or any foreign coins which are by law made current or are in actual use or circulation as money within the United States; or whoever fraudulently possesses, passes, utters, publishes, or sells, or attempts to pass, utter, publish, or sell, or brings into the United States, any such coin, knowing the same to be altered, defaced, mutilated, impaired, diminished, falsified, scaled or lightened – shall be fined under this title or imprisoned not more than five years, or both."
If that isn't clear, this info from the US mint should add all we need-
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 U.S. Mint does not promote coloring, plating or altering U.S. coinage: however, there are no sanctions against such activity absent fraudulent intent."
And if all that isn't enough, just think about our own US National Parks. Who hasn't stuck a penny in one of their little souvenir machines and cranked the handle until it was squashed and imprinted with the image of a national landmark!