It's quite possible to come up with incorrect conclusions using very sound logic. Truth and logic don't have to go together, although logic will certainly result in truth more times than not.
Logic is a process of identying errors in an argument in order to develop an argument without errors. That being said, When the premises that begin the logic process are flawed, the knowledge of the person making the argument in incomplete, it is quite possible to be perfectly logical and wrong.
In a lot of ways logic is a verbal equivalent of scientific method. It isn't about creating absolute truth, it is about identifying and eliminating errors to get closer to the truth.