The good news is, the answer to your question is most likely YES . . . potentially . . . because all countries in the world operate under the same general monetary system as the US, more or less. The problem is, the legal cites in the Liberty system have never been adapted for other countries.
The Liberty system has laws cited, like "USC ยง 1692 et seq", and people in other countries would have to have a lawyer or paralegal find the equivalent for their nation and replace it in the Liberty documents. "USC" is the United States Code, and that only applies in the US -- that's why the introduction said at the top "Mainly for card holders in the USA".
However, this system SHOULD work for people in other countries 100% successfully, just as it does in the US, if one replaces the US laws in the set with the laws from that country. Do you have a lawyer or paralegal who can do that?
So to clarify, it's not the citizenship of the card holder that matters. It is from what country the card itself was issued. For example, if someone is Canadian but has a Visa from a U.S. bank, then that qualifies. The cardholder agreement must be under the U.S. jurisdiction, thus meaning the card has to have been issued in the U.S. for the Liberty system to apply as is, without legal modification.
Also, another method that can possibly work for non-US citizens and residents, is if the card holder in the foreign country can transfer the card balance to a US card. For example, if someone from Australia has $7000 AUD in Visa or MasterCard debt on an Australian card, and if that same person were to acquire an American Visa or MasterCard from a US bank, that person could ask the US institution if it would transfer the $7000 AUD balance from the Australian card to the US card. Most institutions are more than happy to do so . . . because it gives them more business, and therefore more revenues. To them, it really doesn't much matter what country the debt comes from.
Then once the debt is on the US card, it can be cancelled using the Liberty program.