I did have a teacher that also insisted that the eye must be locked on the score nearly 100% of the time. Had my doubts then, and still do, that this is a requirement for fluent sight-reading. IMO, if one employs good sight-reading technique, momentary diversions from the score are very well within the capability of the brain to manage. In fact, there are many real-world scenarios that demand the eyes look elsewhere during performance: conducting from the keyboard for instance.
Another one of my teachers trained me to fluently jump around the score, while maintaining an unbroken musical performance: both backwards and forwards throughout the music. I have found this an extremely valuable tool, that is far more beneficial to real-world use then a strict training of the eyes on the score.
Piano music, I find, requires a certain amount of nimble traversing of the keyboard, and as such a certain requirement to know where to next place your hands. Idiomatic piano writing often includes wide leaps and sudden changes of hand position. When I play organ, I find there is a less frequent need to look down at the keys.
For becoming more familiar with keyboard geography, I find playing in a dark room is beneficial. It is not as drastic as playing with eyes closed. Your eyes still do make out contrasting colours and shapes, but not to the same detail as with normal lighting. Playing at twilight, with an open window, as the light fades is also another great exercise. The gradually changing light conditions put an ever increasing demand on the player to rely on other senses in order to locate keys.