Some of these look like they use self tappers? I would not want to drill holes in the bodywork as this would create a rust trap especially with all the mud about. There used to be some with clamps that are less immediately damaging but still could cause damage if overtightened.

The image does suggest putting the screws through the metal on the lip of the wheel arch. But that is a basic and universal image as opposed to being for a specific car. I say that because when I used to fit mudguards of the moulded type, screws like that were generally inserted into the plastic liner. But even if they were to be screwed into the metal, an extra couple of minutes preparation would (along with the metal being galvanised) reduce the risk of corrosion to the absolute minimum.

But, just to be clear, I wouldn't be drilling holes into the bodywork either, not so much due to any concerns about rust, or simply putting holes in the bodywork, but because I just don't see mudguards or flaps, worth the bother (and I also spend a lot of time driving on muddy rural roads). They may prevent the lower part of the body becoming as dirty as it may otherwise, but they won't keep it clean, so you will still have to wash the car. Assuming you use a power washer to do so, it isn't going to have any difficulty shifting lumps of mud from the sill.