According to quickanddirtytips.com, "The traditional grammar rule states when a pronoun follows a linking verb, such as "is," the pronoun should be in the subject case. ... That means it is correct to say, “It is I,” and “It was he who dropped the phone in shock when Jodie answered, 'This is she,'” because "he" is the same type of pronoun as "I.""
I would guess Murphy follows the traditional rule, so saying "Avery or I" would be correct for her.