Many companies (especially software companies) put something like "[Our product] is used by [Company 1], [Organization 1], [School 1], [Company 2], and 10,000 more!" on their website.
In US law, is permission from these companies and organizations needed to list their use on the website? If the makers include a footnote saying, "use of [our product] is not necessarily an endorsement by the company" does that serve in place of permission?
Note: There are similar questions pertaining to the use of logos, which is not what I am asking about.