The story comes from towing, where the vehicles are often only stable in tension (if weight is poorly distributed or strange aerodynamic loads) and you can damp the oscillation by hitting the gas on the tow or the electric brakes on the trailer. It you try to stop the oscillation by hitting the brakes on the tow, you'll end up in a horrible accident.
The aerodynamic load of a trailer is enough at highway speeds that its like hitting the trailer brakes already if you panic and take your foot off the gas, so if that didn't cause a recovery you're best off flooring it to get the system in tension which usually eliminates sway, then carefully slow down.
People who haven't looked into the mechanical engineering of towing are often confused why 400 pounds of stuff in the pickup bed is no problem but 400 pounds of trailer requires strange elaborate sway bars and brake systems and strange dampeners on the hitch... its a oscillation damper not a total power dissipation issue.
In theory a perfect aerodynamic and weight balance tow and trailer would never fishtail at any speed; in practice of course they do.