I received the same warnings, actually it was more like “don’t trust everything you read on the internet”, but it quickly became apparent that the last three words were redundant, and could have been rephrased more accurately as “don’t trust everything you read and hear and see”.
Our parents and teachers were living with their own fallacious assumptions and we just didn’t know it at the time, but most information is very pliable. If you can’t change what someone sees, then you can probably change how they see it.