You miss the point—he is still hiding it. The eye provides full 360-degree vision at all times, but few people know this, so he maintains an appearance of some level of vigilance.
This means that anyone who sees him respond quickly to a threat (i.e. evidence of vigilance) will have an immediate explanation of how he was able to do so (being vigilant), and not look beyond it to find out the extent of his abilities.
You miss the point—he is still hiding it. The eye provides full 360-degree vision at all times, but few people know this, so he maintains an appearance of some level of vigilance.
This means that anyone who sees him respond quickly to a threat (i.e. evidence of vigilance) will have an immediate explanation of how he was able to do so (being vigilant), and not look beyond it to find out the extent of his abilities.
Quite well thought out, really.