In too fast - need more lean ?

I must be bloody strange. In some of these Life At Lean videos, the guy says ' if you find yourself being in corners too fast, you need more lean'. I do the exact opposite - I trail-brake to lose speed while keeping the bike as vertical as possible to get maximum tyre grip. Then when I judge it is safe, I accelerate to get around the corner. Even a neutral-handling bike will usually steer itself in the correct direction when you accelerate when on a lean. But you usually cannot accelerate when you are on maximum lean.