Yes, humans can move their eyes independently... just watch these videos (link 1 and link 2).
But, how much use is that? What can you see if you cross your eyes? I know when I do it that crossing eyes serves very little purpose other than to help with pulling faces :) Everything just goes blurry and my eyes start to hurt.
One reason our eyes have evolved to work in harmony is because of binocular vision, it's why they are on the front of our heads, not the sides. Depth perception is difficult with one eye; put on an eye-patch, go play catch, see how you do compared to normal.
A chameleon has evolved independent movement of their eyes. The eyes are mounted on the sides of their heads, this is because some of the time they need 360 vision to spot danger. However, because they are also predators using a highly precise method of capture (requiring good eye-tongue coordination) the ability to point both in the same direction, giving them binocular vision, is also highly advantageous, thus they can move them independently to face the same direction. For more info see the wiki page or this article.
With regards to the quote above, you might want to read the answer to this Quora post, one guy says:
I flew the AH-64s for over 12 years. There's no single Apache pilot I
know who can move his eyeballs independently, nor who is required to
do so. Similar to what Steve mentioned, the trick is to learn how to
ignore input from one eye and refer only to the input coming from the
other eye, then switch between them and do this every few seconds.