It is not true.  You may carry a message about your supporter on the website.  The question is whether it might cause you to be liable for unrelated business income tax (“UBIT”).

There is a fine line between advertising and acknowledging a sponsor.  (See Ready Reference Page: “IRS Finalizes Regs Covering Sponsorships”)  The difference for the charity is whether the income is considered a contribution or whether it is considered advertising revenue that is subject to UBIT.  The advertiser/sponsor doesn’t care very much because the payment is deductible either as a contribution or as a business expense.

When you advertise price terms, you are likely in the realm of advertising.  But if the message is merely a listing of providers who provide discounts to your membership, for which you don’t charge specifically, it may be sufficiently divorced from the payment to avoid UBIT.  Even if it is subject to UBIT, you don’t have to report it if your total unrelated business income is less than $1000 a year, and don’t have to pay tax unless you have more than $1000 net.