Not being a numismist, I can't express any great authority here, but I have not heard of any fractional cent US coins, or of any "larger than a dollar" US coins except for very rare ones, none larger than the 20 dollar gold piece of a century or so ago.

A few local jurisdictions did some minting on their own in odd denominations, in areas later incorporated into the US, but have there actually been any of these strange ones minted by the US?

Now IFF one should produce a coin with a value of 7/19 of a dollar, one could have any number of them and not be able to make exact change for much of anything, but I don't believe postulating the existing of never-before-minted coin values, or even of coins not commonly in circulation, is within the scope of the original statement.

"You can always win the argument if you're free to change the rules."
-Anon?

John