The "Beginner Photographer" samples in the article look the best to me, out of all the samples. Is that not supposed to happen?

Yeah, TFA's point is that the basic/inexpensive camera in the hands of an unskilled user can be higher quality than an equivalent iPhone camera shot. In my opinion from the example shots used this is definitely the case. Camera phone distortion is pretty bad (you have to stand back further from your subject offset this, use a higher res setting, and crop in) and the processing has gotten out of hand in recent years to the point where it starts making photos look worse and worse.