pronouns - "I showed the monkey himself in the mirror". Why is this sentence grammatical?

I am asking this question for a homework assignment where we have to explain why certain uses of reflexive pronouns i.e. himself, herself, are grammatical or ungrammatical.

For one of the questions, we have to explain why the use of the reflexive pronoun "himself" in the sentence "I showed the monkey himself in the mirror" is appropriate.

I read from various online websites that we generally use reflexive pronouns as the direct objects when the subject and object of the sentence refer to the same entity.

However, in this case, I thought that the subject of the sentence is "I" and the object of the sentence is "himself". According to the rule, the sentence "I showed the monkey himself in the mirror" should not be grammatical but it sounds correct nonetheless.

Can anyone offer an explanation for this? Thanks in advance!