The way I look at it, it's not that bad. Psycho is a horror classic, and if a kid wants to see it, he/she might as well see it. Yet, at the same time, if a kid below 12 has even heard of this film, they don't need to see it. It does evoke some... fear, in a sense. It isn't "nightmarish," but there can be some post-viewing shivers, if you know what I mean.
In my opinion, it isn't the shower scene that would "get" most parents. There is no nudity, and the violence can only be imagined. I will say that the review is slightly incorrect; if you are looking for it, you do see the knife touching the skin. Alfred Hitchcock had such a mind for things I'm sure he intended this subtlety. The scariest part for me was the revelation of a corpse. It wasn't violent, but it was definitely creepy.
The only "violent" scene was the one in which the private investigator is climbing the stairs in the Bates Mansion, and "Mrs. Bates" comes out and murders him (sorry, spoiler). His face is slashed, and this could be viewed as violence. While I fully realize that the other "slasher" scenes are intending to be violence, modern times have brought children and teenagers to where no blood and no gore is not scary, and not effective. We must remember that this was released in 1960, when it was considered one of the scariest movies of all time. Even the remake (1998) was only slightly more horrifying.
If you know your children cannot "do" horror films, don't let them watch this. But, if you have a movie-loving child, this is a must see. Without Psycho, we would be no where near where we are today, not just with horror films, but with all film.