Gee, I've never heard of anyone getting their eyes infected from using potatoes after burning them. I don't doubt that it could happen, and it would probably have a lot to do with the severity of the burn. Now I'm going to have doubts about eating anything that was grown in the ground including carrotts! Just kidding.
The smartest thing to do is always see a doctor, but sometimes late at night there isn't much choice and that is the reason a lot of people choose to try this. I never thought of it causing anyone any harm. But then I'm not a doctor either.