A player can wear any clothes he/she wants to wear at a tournament. In fact, Kafelnakov has never had a paying clothing sponsor but he almost always wears Nike. Nike has never paid him a penny, as far as I know.
On the other hand, Pete Sampras was dumped by Nike this year but Pete still wore Nike at the Aussie Open and the Davis Cup. However he covered the Nike swoosh with a small American flag. I don't know if he has a new sponsor yet.
I don't know anything about what happen with Haas.
Re: Justine . . . maybe she needed a hat because of the sun and she didn't have a hat from her sponsor. A lot of players wear the U.S. Open hat if they don't have one of their own.
Actually, for quite awhile, addidas used to supply shoes and clothing for those players in the top 50 or 100, without clothing contracts! I have no idea if that is still the case.
That makes sense. Adidas gets free advertisement and the players get free clothes.
I think if an unknown player gets to the semis or finals of a big tournament then some clothing sponsors will give that player a little money and free clothes to wear in the semis and/or finals. The paid sponsorship rarely goes any further than than unless that player starts winning a lot.
But mostly, clothing people try to spot good players when they are very young. Reebok got Andy Roddick when he was 12 years old and I think they got Venus when she was about that age. Rumor has it that Nike has signed a 13 year old boy and paid him a lot of money. They're hoping that pays off better than their contract with Alex Stevenson.