Your version is, to put it mildly, much more common and idiomatic.
It is the source of a popular children's joke:
Q: What's on the television tonight, Dad?
A: Same as usual, Son — the goldfish bowl and some flowers!
The “corrected” version is based on the notion that the first on is what’s currently being broadcast, and the second is describing where it appears. It's not helpful, but at least preempts the aforementioned silly joke.
For those who perceive it as mere tautology, the first “on” means playing, as in What's on at the theatre tonight?, or happening, or up. The second is about the presence of the image on the screen.
It’s not that the teacher is grammatically incorrect, simply that almost no-one says it that way any more.