ANSWER: Apparently, now they are both correct.
My 1998 edition of "Dong-A's Prime Korean-English Dictionary" defines 벌쓰다 as "be punished; suffer punishment; [of a child] stand in the corner," and the verb 벌서다 is not even listed in the dictionary. So, according to my Dong-A dictionary, 벌쓰다 is a passive verb that means "to be punished," and 벌씌우다 is a transitive verb that means "to punish," including the punishment of having a child stand in a corner.
1998 "Dong-A's Prime" Dictionary
However, my 2014 edition of "Minjung's Essence Korean-English Dictionary" defines 벌쓰다 simply as "to suffer punishment," without mentioning anything about [a child] standing in a corner. Instead, it lists the verb 벌서다 and defines it as the punishment "stand in the corner." In other words, my 2014 Essence dictionary separates the punishment of a child standing in a corner from other punishments. So, if a child or person is punished in any other way besides standing in a corner, the verb 벌쓰다 should be used instead of 벌서다.
Not many adults are punished by having them stand is a corner, so maybe the verbs 벌쓰다 and 벌서다 were originally referring to punishments for school children. If a student talked in class, for example, and was told to write 100 times "I will not talk in class" as punishment, could that have been "a writing punishment" (쓰는 벌), and if a student was told to stand in the corner as punishment for something, could that have been "a standing punishment" (서는 벌)? I do not know it that was the origins of the verbs 벌쓰다 and 벌서다; I am just thinking out loud now.
