Oxygen, via oxidation, can be dangerous.I don't see why hydrogen peroxide would be harmful to an apple product unless people are not diluting it down properly. Hydrogen peroxide is H2O2, which is basically water with an extra molecule of oxygen added. This makes it one of the most simple and safest of known chemicals.
I can only think that people are using it incorrectly and Apple just feels the need to cover themselves. Obviously any liquid can be damaging to electrical products, but I genuinely don't see what damage that a 3% H2O2 solution could do on a cloth.