I've got 100 bucks that says I can go to any car lot, start every car, remove every negative cable with the engine running, and not one single one will be damaged.
I realize that repair manuals say not to do it, but the fact of the matter is, 99.99% of the time it won't hurt a thing.
Example: My 99 Tahoe. I start it one morning, drive 30+ miles. Stop to get something to eat. Get back in car, no battery power at all.
Great, I say, dead battery. Get out my jumper and open the hood. Keep in mind this is a GM with side post terminals.
To my surprise, I find that it's not a dead battery, but the actual Positive terminal, the part with the threads that the cable screws into, has come loose, and the whole trip has been sitting there moving around, making contact, and breaking contact. I could push it back into the battery and the truck would start. Drove it back 25 miles to the dealership(it was under warranty), again, with no damage.
No harm done. New battery, ran like a champ. Still does.
If you don't know what you're doing, maybe you should leave it do the professionals, but like I said earlier, removing the NEGATIVE cable will not hurt a thing. I've done it hundreds, if not thousands of times on brand new cars with no ill effects at all.