crossed wire on the turn signal\brake power lead into the park lights
Maybe he is refering to the common mistake of placing a Single Contact 1156 Bulb, in the place for a Dual Contact Bulb; in that case, this exact issue will Happens:
... touch the brake pedal, ALL of my running lights turn on. Take my foot off the brake pedal, everything that just came on turns off.
In such case, one circuit gives power to the other... Very simple.