I've flown business class between the US and Asia and South America many times, and there was no special dress code. There also aren't any special dress codes for domestic first class.
The only special dress codes are for airline employees. Perhaps since she was flying on a buddy pass, she was expected to follow that dress code as if she were an employee, which makes sense. If they give free tickets to employees and their "buddies," then they are allowed to ask them to dress at a certain level because they represent the airline company.
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