Final answer:
The real case that Robert McNamara uses to illustrate errors in belief and perception is known as the Fake Barn Country Gettier case, which discusses how knowledge is not simply justified true belief due to the influence of luck and undetected false premises in the context of a man identifying a real barn among many facades.
Step-by-step explanation:
The case that Robert McNamara uses to illustrate his lesson that "Belief and seeing are both often wrong" is referred to as a Gettier case. This philosophical concept challenges the classic definition of knowledge as "justified true belief" (JTB). One of the examples to illustrate how belief and seeing can be wrong is the Fake Barn Country scenario by philosopher Carl Ginet.
In this scenario, Henry is driving through an area with many barn facades used as a movie set and believes he sees a real barn. While his belief that "That is a barn" is true, and he is justified in believing so based on his perception, the prevalence of false barns in the area means it is simply luck that he looked at the real barn, which challenges the idea that he has knowledge.