I agree with what others have said.
The emphatic (as opposed to complement) use of the reflexive pronoun (as in "I did it myself") is a separate issue, but normally the reflexive pronoun is used as a complement ("object" of a verb or preposition) when the antecedent is the subject of the clause.
I would call the rule semantic rather than grammatical.
When the verb does not require a reflexive pronoun, there are occasional (and unusual) exceptions, mainly in non-formal speech, and usually involving particular emphasis (note that, in the sentence in the OP, the word me is stressed and pronounced slightly differently from the unstressed me). With normal stress, it would sound odd.
The rules may be looser for the first and second person singular, where there is no possibility of ambiguity ("He killed him" would be more ambiguous if him were permitted to refer to the same person as he).
One reason to use a normal pronoun (you, me) as opposed the reflexive pronoun (yourself, myself) might be to stress that the verb is being used in a sense more appropriate for a second or third person.
So "I love myself" would be "normal" – what a psychologist would probably regard as healthy (as opposed to "I hate myself"). Using me rather than myself might indicate narcissism.
