I believe you're being naive by thinking Adidas would just give that exclusively clause up.
E. University agrees that it shall not permit the trade name, trademark, logo,
or any other identification of any person, company, or business entity other than adidas, the University, or, subject to adidas' reasonable right of approval, any recognized governing athletics conference of which University is a member, bowl or other post-season patch, to appear on adidas Products worn or used by Coaches, Staff or Team members. University agrees that in no event shall the trade name, trademark, logo, or other identification of any manufacturer or seller of Products other than adidas be permitted to appear on any such adidas
Products.
Here's the link to A&M contract with Adidas, with minor exceptions our is identical.