The problem is time, glancing at the Sun in the sky is exactly that, you glance at it, or you tend to avert your eyes slightly, if you stare at the Sun directly for any length of time then you will hurt your eyes.
Not because of radiation, but simply because you are looking at something hot and bright. Your eyes contain light sensitive cells, rods and cones, basically the rods see the pictures, the cones see the colours, rods are very sensetive to light, that is why when you see at night you tend to see things as shades of grey, black and white, the cones are less sensitve.
Staring at the Sun overloads the rods, this can stop them working, and therefore blind you at least for several days, and possibly for life, and even if your sight returns it may not be as good as before.
Using any kind of magnifying lens, telescope, or binoculars to look at the Sun will within seconds permanently blind you.
Therefore, never stare at the Sun, not even during an eclipse, the period of totality is so brief that to do so puts your sight at risk.
By the way, I have just checked the Wikipedia page, this contains the same error about radiation affecting the eyes, the only radiation that reaches the Earth under normal circumstances is the light we see by, this is very heavily defracted within the atmosphere, hence the blue sky, and is only harmful if you lay out in it and get sunburned. (Oddly, this is what happens to your eyes from staring at the Sun, but as the retinas in you eyes have no pain recepetors you cannot feel the burning unlike on your skin).