Although I cannot point to any particular reason why they chose grey, other than apparently a decision that it was a militarily useful color (their uniforms were Field Grey), I can fix one slight misconception.

Panzer grey, such as it is, was a color found only at the beginning of the war. During the invasion of Poland, they were generally a two-tone scheme of Dark brown and dark grey. It does not show up well in black and white photos. In 1940, the base color became black grey. This stayed around for about a year.

Come 18 Feb 43, all vehicles were to leave the factory dark yellow, with red brown and olive green to be applied by units in the field to suit local taste and requirement. This lasted until August 44, when the camo was painted at the factory, usually the ambush camo.

Finally, by the end of 1944, paint began to become something of a lesser priority in the resource acquisition department. Some tanks were leaving the factory in the red oxide primer, with only a basic coating of camo on top.