Well... it's technically not correct, but IMHO it's "less incorrect" (т.е., не звучит настолько безграмотно) compared to Me and my friend did this or We saw she and John kissing in the park. Which is to say that many educated speakers would not even notice the error if you said, e.g., His father and himself manage the family business -- although "His father and he manage..." is the proper form.
By the way, I would agree with the advice from "Grammar Girl" -- when you're not sure which form to use, try rephrasing the sentence to change a compound subject or object to a singular subject/object with only the pronoun: "Me did this"; "We saw she in the park"; "Himself manages the business."