People attacked with such violence do not as a rule, retrieve small items dropped when attacked, (such as a sandwich) and take them home with them as Smollett admitted to doing. They leave such items at the scene. Adrenaline rush tends to kill appetite immediately and for some time after, then a feeling of exhaustion is a usual secondary-reaction, not hunger.  

The fact that the moron took the sandwich home (presumably to enjoy when he got there) further discredited the validity of his claim as far as law-enforcement investigators were concerned. It demonstrated that in fact the whole thing was not traumatizing for him at all, but rather something that was apparently no big deal emotionally. 

That reaction is similar to how detectives view supposedly "close" relatives or loved-ones who are not highly upset when they learn of their loved-one's murder. It's a BIG red flag (directly from elementary psychology on, "normal/abnormal affects").