Okay, I found the wiring info my friend gave me. Reading it, I think I might understand.

He highlighted the following:
pink/black-Ignition (fuse 16)
pink/yellow-Accessory (fuse 17)

So, how about this: A wire which is energized when the remote start is activated needs to be run to the accessory and ignition wires in order to power the items that are normally powered when the key is in one of those positions. The fact that the pink/yellow wire happens to go to the fuse for the stereo is merely coincidence.

Is that possibly the answer?