the logic test—do you agree?

Even after hearing the answer's explanation, I still don't understand. Maybe the way people talk when they talk about logic is beyond me. Feel free to school me in the comments. I'll leave my own thought process between a set of brackets. Highlight to see my thinking.

[What I'm stuck on is the term "vacuously true." The example that Presh Talwalkar gives is of a room with no cell phones in it. One claim is that "All the cell phones in the room are off." Another is that "All the cell phones in the room are on." Talwalkar claims that both of these statements are vacuously true because, in fact, there are no cell phones in the room, so you can presumably say what you want about imaginary cell phones. 

Now, to my prosaic mind, truth is often about correspondence to reality—what is called the correspondence theory of truth (which obviously doesn't apply to abstracta like 2 + 2). If I claim the sun is shining right now, you can go to a window and check whether the sun is shining. If it is, then my statement corresponds to reality and is therefore true. By this standard, there is no such thing as "vacuously true." If a claim refers to cell phones, but the cell phones in question don't exist, then the claim doesn't correspond to reality and is thus false. So someone will need to explain to me, in little words that a five-year-old can understand, how the term vacuously true works and is applicable. I'm stuck.]