If you write "Went for a burger, meet me there!" and expect the other person to just infer that you meant McDonald's, you failed.

Yes, and that would have made sense to me. But I take the wording 'If you leave someone a note to meet you at McDonald's' to mean that it said McDonalds in the note. If it had said 'a note to meet you at a burger joint' I wouldn't be confused, here. Which just goes to show that there are multiple reasonable interpretations of a text, I suppose.