it actually doesn't qualify as such.

In Monty Hall, the professor would have known you picked A and never eliminated that option even if it was not one of the correct options, so switching gives you a 2/3 chance of being right:

1.You pick A, A is right, professor eliminates B or C. You switch and you are wrong.
2. You pick A, B is right, professor eliminates C. You switch and you are right.
3. You pick A, C is right, professor eliminates B. You switch and you are right.

In this case, professor doesn't care what you picked. He can eliminate the choice you already picked. If you had picked C he still would have said C was wrong. That leaves 2 options (assuming you can trust him):

1. You picked A. A is correct. You switch and you are wrong.
2. You picked A. B is correct. You switch and you are right.