It won't be grey, they'll be dark yellow, red-brown and and a shade of green. SS PzAbt 501 Tiger IIs would have come direct from the factory painted in the standard ambush scheme, using supplied patterns. Those tanks were built October/November 1944 and delivered at the start of December then almost straight into action. The photos of that period all show the factory standard scheme for those tanks.
There is some nice research here
http://www.network54.com/Forum/47207/th ... -+Overview
I would really doubt any King Tiger ever had the slightest drop of grey on it and remember, most of the pictures you see are artists interpretations and should generally be ignored unless they state a source photo. The 2nd image is a pretty well researched one though and is from a Jentz and Doyle book and is backed up by other research on the topic.