Well done. Coincidentally, I think my first frustration regarding (different meanings of) understanding was about that exact issue, back in high school. When my friends and I had learned about the Doppler effect, we were all at Level 1, maybe with minor inroads into Level 2. The problem? I classified that as "not understanding", while my friends called it "complete understanding". So we had conversations like this:

me: Okay, I don't really get this Doppler effect. I mean, why should coming closer make the pitch higher?
them: Because the equation says...
me: Well, I know the equation, but I don't get it at the gut level. What is it about moving closer that shortens the waves like that?
them: Because it like, compresses the waves.
me: But why should the sound wave act like some stiff rod connecting me to the car? Why do you get to apply that kind of reasoning to sound waves?
them: Because that's what the equations say!
me: Argh!

Btw, another important thing about Level 3 is that you could change the question to "... low-pitched when they are coming toward you ..." and vice versa, and the Level 3 rationalist would still derive the same result, except to add that, "wait, I'm confused -- are you sure you're reporting that right?"