I misunderstood how the smart stay feature works in the S3. What happens is, the eye icon in the notification bar pops up whenever the screen is about to time out to see if you're still looking at it. If you are, it stops the screen from going off. It works PERFECTLY now that I understand how it works.
I was under the impression that the eye stays in the bar the entire time you're looking at the screen, but that's not the case.
Looked at my phone for about two minutes with the screen timeout set to 15 seconds. It didn't turn off. Then I put my phone on the desk and... it still didn't turn off (it could see I was looking at it from an angle), so I hid from it and it turned off.
I spent too much time arsing around and trying to get the eye to pop up in the notification bar rather than just reading something to see if it works.
Very useful feature.