"She put on a sad expression."
Translation:Ella puso una expresión triste.
I am saying:
Reflexive form of the verb "poner", which is "ponerse", has a narrow meaning that only includes putting on clothes. You cannot use it for a facial expression, unless you are being very figurative in your speech.
Reflexive forms never mean the relationship that Peli describes, therefore, his conclusion is wrong to begin with. In the sentence "She put it on herself", which he uses in his reasoning, "She" is the subject, "it" is the direct object and "on herself" is the indirect object (technically, the way it is presented, it is an adverbial phrase, but let's allow it). The subject and the indirect object are the same person, true, but that's not what reflexive verbs are, as they mean the subject and the direct object is the same.
With these two things in mind, the provided translation is completely correct.