The good thing is that now known that supplying 5 volt via the 5 volt pin is now officially not OK.
I don't think you can come to that conclusion from those comments.
Powering an arduino with 5V through the 5V pin is fine, providing that is what you do. Powering the arduino from a bunch of batteries no matter what they say on the side can be a problem if the real voltage is greater than 5.5V.
I have a powerplug going from the 12 volt to the Arduino. However when I use this plug the Arduino becomes hot (At the power conversion chip)
Yes it will it is burning off the excess power in the form of heat. With 9V there is not so much to burn.