It's definitely not true that as long as you get the angle right you can't harm yourself with a razor blade.
A very sharp blade will generally shave closer, but as skin isn't a perfectly flat surface, it's always a compromise - the closer you try to get, the more you're risking taking off skin cells along with the hairs, from all those surface protruberances (under a microscope, skin looks more like the Rockies than the Bonneville flats).
How much of that people can tolerate is very much an individual thing. For some, a very close shave from a very sharp blade is fine, for others they get noticeable but acceptable irritation, while still others suffer severe razor burn.
For me, a Feather blade is fine (I have quite smooth and not especially sensitive skin), but they don't last very long - and there are others that are equally effective for me but which last a lot longer.
Alan (BOTOC brother, LOSER)