Chelsea actually had her braces done by a good orthodontist. (I am working from memory here because my kids orthodontist was his best friend and he told me about it.) When she was about 2/3rds the way through her treatment, Hillary demanded that the braces be taken off. The orthodontist tried to reason with her about how stopping the treatment before it was finished and that Chelsea would forever have a bucky look.
Later, Chelsea had plastic surgery to move the jaw to make the look less apparent. But it is still there. That is what her orthodontist meant when "she would have it forever."