When checking the authenticity of a website, I always look at the fine print. Any legitimate company will have links to their Privacy policy and Terms of Use, usually at the bottom of the page.
The privacy policy link on this Hilton Select site goes to the main Hilton Worldwide Privacy Statement. But, the Terms of Use provides the real answer to who runs the site:
The Hilton Select program and this website are operated by Teleformix, LLC a Delaware limited liability company (the "Provider") for the benefit of Hilton Resorts Corporation a Delaware corporation d/b/a Hilton Select and a subsidiary of Hilton Worldwide, Inc., ("Hilton").
For what it's worth, Teleformix has been an accredited business with the Better Business Bureau since 1/1/2010. They have an A+ rating.