Head movements in terrestrial birds

     Wow, really sounds scientific.  I was reviewing some footage of a Solitary Sandpiper, and couldn't help being struck by the way the bird would move it's head back and forth while looking at me.  We've all seen this millions of times.  I've always written it off as a nervous movement prior to taking off or running away.
Turns out there may be a better explanation. (Not mine, I read this.)

       Many birds, shorebirds for example, have their eyes situated to get the best view in as many directions as possible at once.  Thus the eyes are set high on the head and on opposite sides. One eye looks north, the other, south. Unlike raptors, binocular vision is impossible.  No binocular vision means lousy depth perception.  So how do you tell how far away that guy with the camera really is.  One possible way is to take your one eye (the one on the side where the guy is) and move it a short distance.  If your brain is capable of taking the image from head position 1 and that from head position 2 and combining them, you get a 3D image...just like 3D glasses.  Voila, depth perception! Up and down, side to side or something in between doesn't matter.  Can a bird's brain do this?  I don't know, but for an organ that can sleep one side, while the other is awake (as in long-distance migratory flights), it seems like a trivial task.