I don't know about a 20 minute rule but I do know that airlines are obligated to rebook you based on availability or refund your ticket cost if they change your flight times to something unacceptable to you. Usually this would be an option pursued by people who's flights have dramatically changed to the point that they can't make them (ie-changed from an evening to an afternoon flight and they can't get out of work to make the time, etc.).
Would you really pursue cancelling your tickets for a refund over a small 20 minute change? That seems extreme but before you do, check the current rates to make sure you aren't going to end up paying way more for a new ticket.