Why does this SAT question make grammatical sense?

Here is the rule for using I and me. In any situation where there is another person or thing involved, take them out, and resay the sentence. For instance, if I were to use your sentence as an example I would remove the tutor, and resay the sentence - The regularly scheduled conference (for) me is set for... Or would you say (for) I is set for... Of course in this instance, "me" is correct, therefore that part of the sentence is correct. Another example: Me and my mother love ice cream. Remove the other person and resay the sentence.... Me love ice cream, which is obviously incorrect. That means that the correct way to state that sentence is I and my mother love ice cream. But, this is just an example. The etiquette instructor in me says to always put the other person first, which would turn that sentence into My mother and I love ice cream. Hope this helps.