At best I can guess what's going on with your teachers. (Caveat, I'm a nonnative speaker.)
I think most people will understand you quite well if you say, カバンに本があります.
However, from the perspective of the other teacher, different ideas might be going through their head. In English, we have somewhat specific prepositions to make clear what we mean. We can say "there's a book in the bag". That corresponds to カバンの中に本があります。We can also say "there's a book on the bag" (imagine that bag is placed on a table and you placed the book on top of it). This would correspond to カバンの上に本があります。
This last sentence, in English, might sound a little bit weird. It's not what you necessarily expect to hear (you expect to hear "in"). So, if your student (pretending we're teaching English) said, "there's a book on the bag", you might correct them to say "there's a book on top of the bag". Why? Because depending on one's native language, someone might say "on" when they should really be saying "in". Or, you, as the teacher, have an unconscious bias for expressing this idea in a particular way.
I suspect that, if you meant, "there's a book on the bag", it would be better to say, カバンの上に本があります。 But, even if you said, カバンに本があります, and the person you're speaking to can see there's a book on the bag, you'll be understood.
I get it, you're not asking about カバンの上に. But, I am trying to tease out why two native speakers might have different ideas of the best way to instruct the student.