'The student is always right' - This is not a good phrase to use and quite destructive to learning. Why for would we thus seek teachers?
More accurate would be to say a student learning with a teacher is a two way process. There are many different aspects to learning. Sometimes it needs to be a didactic approach, sometimes it is facilitatory.
Teachers may learn something new but to say 'a student is always right' is definitely not on the cards. We can have students who are disrespectful or insulting. Should this type of behaviour be validated by 'the student is always right'?
I think the student is always right. If the student seems to be wrong, then the teacher has to find another way to explain it. It's a counsel of perfection, I know, and language teaching and learning does involve some level of frustration.
In my experience, many Russian students have studied English grammar for years, whereas we native-speakers generally have not. Such students will be able to test your knowledge of grammar to its limits, and expose any shortcomings. Can any teacher say that they have never been caught short on their grammar by a student?