They would have to be hybridized with jenday colors to get a more red like color... however, I would believe that the red factor suns are also natural mutations!
Just don't confuse a kakariki (or what I believe to be one, as that's the only thing it appears to be) with the sun!
http://feistyhome.phpwebhosting.com/kakariki_rob.jpg
http://www.ccpetshop.com/images/DSC00029.jpg