The Wikipedia entry on depth perception (an excellent read) lists ten different cues that your brain uses to figure out exactly how far away something is. Parallax is just one of them. Since the various movie and television display technologies only offer parallax-based depth cues, your brain basically has to ignore several other cues while you're immersed in the world of Avatar. This is why the 3D of films doesn't feel quite right.
I agree that 3D films often feel a bit weird, but I'm not 100% sold on his idea of why this should be. The Wikipedia article names many visual cues that are present in 3D movies as well (e.g. relative size, perspective, texture & lighting etc.). It seems conceivable that your brain is "tricked" and has to adapt to the new situation, I just don't know if his reasoning is valid.