I see no contradiction between the two methods. Use both. After all we are not blind!
Also I think it is important to look at one’s hands (not when sight-reading, of course). I believe in having as little unnecessary limitations as possible. If you are used to playing without looking at your hands, looking at them can really throw you off. Likewise, if you are used to playing using a score (even if you are not necessarily reading it, just staring at it), removing the score can be a real impediment. And the reverse is true. Just try to play that piece you memorised by following the music. It takes a while to adjust. So, when I learn a piece, my aim is to be able to play it is as diverse situations as possible. I should be able to play it perfectly by reading the score, but also form memory. With eyes closed but also by looking at the hands to see their movement and the pattern of keys being depressed sequentially.
Peripheral vision is very interesting because you cannot focus. Unlike foveal vision which will give you a crystal clear picture, peripheral vision is very foggy. It will not be very helpful to precisely locate keys, but it will certainly help to direct your hands to the proper area of the keyboard. Peripheral vision on the other hand has a huge advantage over foveal vision: it detects movement with great efficiency. It is the vision one uses in the martial arts, since you will be able to detect minimum movement patterns from your opponent. Using foveal vision in a fight will get you beaten up every time. Juggling also benefits enormously from peripheral vision. If you look at superlative jugglers, they are always staring straight ahead and using peripheral vision to check the balls/clubs/torches/chainsaws.
I don’t really imagine any piano situation where this advantage of peripheral vision over foveal vision would come in handy. However, as I said, we are not blind, and if you have a piece with big skips, every little help helps.
Best wishes,
Bernhard.