Another thing to think about... Anthony Zerbe plays alot of low key baddies. That is another reason why I say that Councilor Hamann is not all totally with the people of Zion. He doesn't sleep, he walks about alot at "night" and he visits the engineering section. Plus he countermanned Lock. Interesting.
Not stupid but unable to identify. They are not able to identify cyborgs.
Supposing that Councilor Hamann is a cyborg sent by the Great Machine to infiltrate Zion, then he can wreak tremendous havoc there. Would he have access to the Zion mainframe and other vitals of Zion. Then the conversation on the landing with Neo was smoke. He was lying when he said that he has no idea how the machines in the environmental section of engineering work. But he was plumbing Neo for his feelings and standing on matters in general.