Usually to discharge the system and protect the equipment/installer by leaving an open circuit in the system.
It's not super necessary, but if you're installing an amp and you don't get exactly on the terminal you can expect some sparks. I recommend doing it for as simple as it is, and the headaches it could save you should you mess up and ground a positive wire.
Takes all of 3 minutes to remove/reconnect the negative lead from the battery from the time you walk out side and pop the hood to the time you reconnect and close the hood.
I think it's more to protect against any wire getting scraped and stripped against the chassis and grounding out... I can't see how there'd be any risk working with the aux input itself since the radio would be OFF and not even getting ignition power. It's just wise to kill the power from the battery any time you're moving stuff around under the dash in case you nick a wire that's got power on it.
I wish I had a solid technical reason that I could type up and would make perfect sense but I'm having a hard time putting my rationale into words.
Basically, if you have the battery still connected you have a closed circuit. If you are adding devices (amps especially) and happen to ground the power wire (which is based off the battery's + terminal) you've just shorted the electrical system. More than likely you'll get sparks and a good scare and not much personal or vehicle damage. On the other end of the spectrum is scary consequences like getting shocked and hurting yourself severely, or even setting fire to your car.
That's where a fuse comes into place. If you have a fuse upstream of the wire that's shorted more than likely the fuse will blow and you'll shut the circuit down. However, if you don't have a fuse welcome to fire. Ever heard the horror story of someone's car catching fire with an aftermarket setup? Most likely there was a short in the system and either the fuse wasn't the right one, or there wasn't one at all... POOF! End of system, end of car. This actually happened to a "jerry rig everything" friend of mine. Lesson learned.
Like I said, the chance is unilkely, but there is a chance. Especially if there's a long stretch of wire that's not fused, or even a small stretch that's not fused. It's better to just play it safe and disconnect the battery everytime.
Here's an interesting quote from my JL 1000/1 amp manual:
"Disconnect the negative battery post connection and secure the disconnected cable to prevent accidental re-connection during installation. This step is not optional!"
In the case of the aux wire, you're probably fine, though. As long as you've got a fuse you should be alright.