It's even worse than that.
You each have four flags. The first flag is black on one side, red on the other. The second is black on one side, green on the other. The third is white on one side, red on the other, and the fourth is white on one side, green on the other. (In other words, one side is black or white, the other side is red or green.)
The flags have the peculiar property that as soon as they are exposed to enough light to see what color they are, they burst into flames. So you can look at one side of a flag, or the other, but you can never see both sides of the same flag.
You and your (entangled) friend each choose a flag. The alien observer observes the following:
1. Your choice of flags, considered independently of your friend's choice, is indistinguishable from random. Likewise, your friend's choice of flag, considered independently of your choice, is indistinguishable from random.
2. Nonetheless, if the alien looks at the black-white side of both flags, they are always the same. Likewise, if he looks at the red-green side, they are always the same.