Deeday, I am astonished to read what you said about your instructor.
Good news, you've finally understood why it's good to always have a transponder turned on to Mode C. And what helps us sometimes is exactly the reason that your instructor was blaming, and that is the fact that *every* transponder uses 1013.25 as their reference. This is fundamental for TCAS, as what matters is a relative altitude and not an absolute one.
Really surprised someone could teach with such a gaping hole in her aircraft knowledge...
Ciao, Luca