Wow, that's bogus. No, you can leave a laptop plugged in. That's... I don't know why someone would say that. I would say hold the power button down for like 30 seconds and see if that clears it up. Just a thought. Normally, I'd say pull the battery out and let it sit overnight, but that doesn't seem to be an option anymore. You can absolutely leave it plugged in.
I can sympathize with you. My power supply with trip a breaker when I plug it in, but not the breaker of the circuit I'm plugging it into. Support wants me to mail them the entire laptop so that they can RMA the power supply. I love my new G752VS, but I'm really not loving Asus support. I really held a higher standard for support with a $2200 laptop, but so far it's worse than Dell's. Since shipping isn't free and I have to insure the package on my own, I'm looking at about $80 just to ship it to them with an unknown turn around time. That's more than half way to just buying a second power supply outright. 😕