Now adays the Haig would lose a great deal of sponsor money if he didn't wear a sponsor-logoed hat of some description. In his book The Walter Hagen Story, Hagen did speak of one particular incident where he did put on a cap--at least for one shot in particular. Hagen writes:
"I did, however, borrow a cap temporarily during the last round of the PGA at Dallas in1927. I was playing against Tommy Armour, and had him 4 down going to the thirteenth hole. All during the tournament I'd been closely followed by my caddie on one side and a most enthusiastic young boy about twelve years old on the other side. As I squinted at my ball before taking my second shot, I remarked to my caddie, 'This is one time I wish I had a cap.'
Immediately my young golf fan stepped forward and very politely offered his cap--a baseball type, peanut-size cap with his school insigne on the bill. It was just about big enough to shade my right eye and I wore it cocked precariously when I made my shot on the green. The gallery got a laugh when it almost dropped off onto my ball, but I got the shot away. I then walked over, thanked the youngster and assured him I'd never have made the green without his cap. I won the match from Armour 5 and 4.
A dozen years later, in 1939, at Pomonok Country Club at Flushing, Long Island, I was playing in the lower half of the PGA Championship against Tony Manero. When I had holed my ball on the home green, a very charming lady stepped over and introduced herself as Byron Nelson's mother. She reminded me of the small boy who had followed me so diligently around the course at Dallas in 1927 and whise cap I had borrowed.
'That youngster was my son, Byron,' she told me."
The Haig wrote that he hoped he had given Byron some of the inspiration that led to his becoming one of "our top ranking golfers." I reckon he probably did.