They made an error. 30-day extension runs from the date of expiry of the entry stamp, irrespective of when you apply for it. I know some people apply for the extension only a couple of days after they arrive in Thailand
Actually there's nothing in Thai law which states three months. It says "temporarily in the kingdom", which can apply to any temporary visa. Hence I've driven for 12 years in Thailand with my Australian licence and never had a problem, as I have to extend my temporary extension every year, I'm only a temporary visitor