My younger doxie, Blue is also on thyroid meds.. and it does help keep her from being a butterball. Her coat is better also, it had been thin around her tail, I'm ashamed to say my groomer noticed it and suggested the thyroid test, even though I was working at the vets at the time! ( It was just mild thinning/ slow regrowth by her tail)She also has allergy problems, poor doggie.

Anyhow, it sounds to me like the golden's owner in question is either not treating the problem, just started treating the problem, or using it as an excuse to allow her dog to be overweight!