It's actually not a very valid take at all. It is VERY clearly not black I suggest your monitor is extremely poorly calibrated if it appears so. It not only isn't a crescent its not even a vaguely crescent shaped object. In Muslim iconography the crescent is a moon an object in the foreground not the background formed by putting any circular item offset inside any other.
The logo is black, which seems to qualify as "green or black"?
Red and white are also very common (ottoman flag, turkey, tunisia).
> I don't recollect them using stars either.
"Star and crescent" has been common muslim iconography since the 14th century, and the ottoman empire (which introduced them).