I dont think that is true.
I presume you are saying you do not think it is true that most people in occupied Europe would not know about the death camps.
How would they know?
The camps were a closely guarded secret.
Information was tightly controlled, even in the United States.
Most people believed what their leaders told them.
The Polish Underground managed to get out a report to the allies, with pictures and an eye witness account, in 1944.
The Polish officer who delivered it wrote it up as The Story of a Secret State: My Report to the World.