In his book Unlimited Access, FBI agent Gary Aldrich, who was assigned to the Clinton White House, describes Hillary Clinton’s instruction to the White House staff to never look at her. “When ‘Queen Hillary’ walks down the hall, you’re not supposed to look at her. She doesn’t want staff ‘seeing’ her.”
I live in a city of less than 200,000. I know of 2 prominent CEO's (one now retired), who had these quirks. One of them issued a memo saying that if employees should encounter him walking down the hall, they shouldn't speak to him unless he speaks first, so that if he's thinking an important thought, they won't break his concentration. Another CEO had a carport and private outside door built adjacent to his office, so that he and only he could come and go in private. This same CEO refused to walk down the hall alone (had around 500 employees) during business hours. If he needed to attend a meeting outside his own office, or just go down the hall to stretch his legs, etc., he would have 2 or 3 of his closest aides accompany him just for the walk. Neither of these CEO's were heading their "own" companies.