Generally, published rates mean those rates made available to the public via travel agents and public reservations service like Expedia, Orbitz, Travelocity (speaking for the U.S.). These rates would also be available from the Hilton.com website, but so would website "internet only" rates, which should be noted as such and would, I suspect, not be published rates.

If I were doing this, I'd research the rates first, so that I'd know what type of rate the "hotline" was offering me. And just because they don't offer the lowest rate at first (a common tactic) doesn't mean you can't ask then for the lower published rate you found.

I wonder if Hilton USA has a similar program?

(FYI, there are two separate companies: Hilton Group plc, aka Hilton International, based in UK, and Hilton Hotels Corp., aka Hilton USA/North America. Both are publicly traded, and they share marketing operations in an attempt to appear as one company to the customer. The benefits described herein are pertaining to Hilton Group plc.

Try these links:

A little history

International: Hilton Group plc

N. America: Hilton Hotels Corp.