Is it simply a merger of grey and beige? 
While reading about Murphy’s Law you may run into a great truth: “anything is more complicated than it looks before” 
.
As I first read your post I would’ve bet that the etymology you proposed was the obvious one and only… but than, just in case, I checked on the Merriam-Webster and found:
" Etymology
Adjective:
borrowed from French grège “raw, unfinished (of silk),” going back to Middle French, borrowed from Italian greggio (Upper Italian grezzo) “in its natural state, unfinished,” perhaps going back to Vulgar Latin *gregius “plain, ordinary” (formed as a counterpart to Latin ēgregius “outstanding, first-rate”), derivative of Latin greg-, grex “flock, herd, troop”; later construed in English as a blend of gray entry 1 and beige entry 2 — more at egregious
Noun:
derivative of greige entry 1
First Known Use
Adjective:
1835, in the meaning defined at sense 1
Noun:
1911, in the meaning defined above"
Yeah, the world is full of surprises… 