So do you want to become a free mobile advertising billboard for your suppliers.
I, for one, generally use the t-shirts supplied by suppliers for rags.
I would rather have myself and employees wear t-shirts with my company on it that wear a supplier t-shirt advertising their company.
If they want their product on my website - they can pay for it as far as I am concerned.
PS - I do not have any quibbles about using coffee / tea cups supplied by suppliers