This is not quite true. Reading via peripheral vision is a skill, but most people never have the right kind of motivation (and perhaps not the right kind of visual stimulus) to learn it. I know this because I have personally known someone who read exclusively via her peripheral vision.
There's an inherited retinal disease that runs in my family. It's a form of 'cone-rod dystrophy'. Cone-rod dystrophies are diseases where the cones and the rods in the eye eventually stop responding to light. The order of the terms in the naming reflects the typical order of the dystrophy: first the cones (responsible for central vision) go, then the rods (responsible for peripheral vision) go, too. As the cones and rods go bad, this results in loss of visual acuity in central and peripheral vision respectively. (It often causes lots of other, less generic problems, too, such as: blind spots, warping/twisting distortions in the visual field, sometimes flickering artifacts, progressive colorblindness, extreme light sensitivity, and an effective reduction of contrast.)
Between individual cases, there's a lot of variation in how the disease presents. There's no fixed timeline or ordering for the progression (even though the disease's genetic cause has been identified as just a single gene!).
Anyhow, in my late aunt's case, her central vision was useless long before her peripheral vision could give out. So she learned, somehow, to do things like read her smartphone using only her peripheral vision.
We chatted about it once or twice. Onlookers often could not comprehend that she was looking at her phone, since her eyes weren't pointed towards it. She once laughed to me about how someone had asked her 'Why are you sniffing your phone?', while she held it up to her face to read a text message.
My impression is that learning to rely on your peripheral vision in this way is extremely counter-intuitive and difficult to do. (This may have something to do with the mechanisms discussed in TFA.) I wonder if it can even be done at all without first obscuring one's central vision (which I guess you could do artificially with contacts). But evidently it can be done.