Not addressed to anyone in particular, but if you're pulling a trailer which is already unstable and beginning to fishtail, applying the brakes could easily exacerbate the fishtail.
Think about it... what happens when you apply the brakes. The vehicle slows but the weight more-or-less transfers forward toward the nose. If the vehicle is tail-heavy or turning a little the backend will want to slide around and forward, and it's worse in the rain or snow. By the same token, if you've got a trailer which is already moving from side to side, any slowing at the swing point (the towing vehicle and the hitch) can result in the tail coming further around due to the inertial whipping action of a trailer already moving laterally.
Those of us advocating speeding up slightly aren't talking about hammering the throttle, but of simply increasing speed slowly and slightly in order to "pull" the trailer out straight, getting the nose of the trailer moving a little faster than the swinging tail and thereby encouraging the trailer to follow the nose and reduce the side-to-side motion. Once it's straight you ease it back down to your cruising speed.
Not the most scientific explanation of course and certainly not trying to start any sort of flame-war, just wanting to help safeguard our members here.