Yes, but you don't owe them any money if you want to buy something. From the link:
"There is, however, no Federal statute mandating that a private business, a person, or an organization must accept currency or coins as payment for goods or services"
but if you are going to quibble and point out myths and misconceptions, why not just tell the whole story instead of half of it. If you eat in a restaurant, and they tell you "cards only", you owe them money, and your cash is good. "good for all debts, public and private" has a meaning that is not vitiated by a "no cash" policy.
