For any product, if there is a substantive processing step done (other than basic packaging), I would consider the label to be accurate.
Additionally, mandatory COOL seems like a self-serving overreach by the cattle industry. By all means, include optional labeling specifying the country of origin, following whatever (non-fraudulent) criteria you want, and that label can be protected all you want, but don't make it mandatory.
Shades of the equally ridiculous mandatory GMO labeling that thankfully got nixed.