My impression is more that here is a middle-aged or older woman, who a week ago was living an ordinary, mundane life in a rural part of Pennsylvania, and suddenly the bottom has dropped out of her life.
I think she covered her face, JMO, due to being overwhelmed. She hadn't prepared for a life where photographers from all over the country are trying to take her picture, reporters are going to be shouting questions at her, and people everywhere are judging her and her husband.
If she privately harbors doubts about her son's innocence, that's for her to know, but I see covering up as a self-protective maneuver and not because she's sure her son is guilty.
It's an action that to me screams "make this all go away."
IMO