Each team/country has a kit sponsor that they had to wear at all times but if they have individual gear sponsors they can wear them in competition.
Although the team is sponsored by Nike, a rider can wear Adidas/cons/vans etc while competing but must revert back to Nike's if/when they appear on the podium.
No alternative branding can be worn on clothing including headwear.
The USA basketball team players will all wear their respective sponsors shoes while playing but when not on the court they have to wear Nike.