"My parents thought that you were our teacher."

Here the English is ambiguous. "My parents thought that you were our teacher" could mean
a) they thought you were currently our teacher b) they thought you are the teacher that we used to have. i.e. they thought they recognised you but got it wrong**

Am I right in thinking that Russian does distinguish between the two interpretations, and would use был(а) in the latter case?

why does it not "мои родители думали что ты был нашем учителем"?

"Мои родители думали, что ты наш учитель" is fine too.

were прошедшее время are настоящее это к модерам хватит спать