Hazel has a perfectly "normal" intelligence, which means she can only think in short bursts. George wears a radio device in his ear through which the government transmits noises to disrupt his thoughts so that he cannot take unfair advantage of people like Hazel by using his brain.
Hazel, who wears *no* handicaps can't recall what she has witnessed because she is "normal". In the government's attempt to create equality, every member of society has been reduced to the lowest common denominator. Normal people, therefore, are not very smart, strong, or agile.
George never witnesses Harrison's death. He was in the kitchen getting a can of beer, so he depends upon Hazel to tell him the news. She is so "normal" that she can't remember what happened just moments ago. However, even if George *had* witnessed Harrison being shot, his ear radio probably would have prevented him from thinking about it much, though he may have remembered the incident.