No, it's not "gaining power through a short"; and yes, it shutting off by your pulling the fuse proves that.
The DRL module takes power from the battery (through the fuse that you pulled) and it pulses that power very rapidly (I suspect it's just a control circuit and a big power transistor) and sends that pulsed power to the headlight hi beam filaments. This causes the headlights to light, but at a reduced level whenever the ignition switch is on. Turn the ignition off, or turn the headlights on manually, the DRL turns off.
Your DRL module has failed, because the transistor is stuck "on" all of the time. Pull the fuse, you're removing the power to it.
I think that somebody posted the schematic for the headlights; look it over, follow the circuit paths, and hopefully things will make better sense.
Don't sweat it, man. Look at the bright side; the more your truck breaks, the smarter you'll get.