That is not consistent with my experience. TRAILER brakes pull the rig back straight. Truck brakes make the rig jack-knife if the rig is already swaying or side loaded. That is why brake controllers have the override button on them. It is there so that you can apply trailer brakes without applying truck brakes.I hope that is just a poor attempt at humour! Brakes when a trailer is trying to pass you is a bad choice.
The momentum makes the trailer swing side to side since it can't go forward thru the vehicle. Brakes just causes it to whip even harder the other way.
The side to side motion issue is often caused or made worse by improper weight distribution. The complex explanation involves discussions of harmonic dampening & gyroscopic stability. The easy answer is to keep the mass in the trailer centered, a little forward of the axle center & keep as much of the mass as possible away from the outer reaches of the trailer.