I believe the wording on the UA web site is outdated (that rule was enforced briefly, then UA backed down). The current wording on the Star Alliance web site is:

"Star Alliance Gold members and a guest can access lounges around the world -- no matter which class of service they travel in! Just look for the Star Alliance Gold sign outside the lounge and present the ticket for your same-day Star Alliance flight, your boarding pass and your frequent flyer programme card featuring the Star Alliance Gold logo. Guests must enter the lounges with an eligible Star Alliance Gold member and must depart on a Star Alliance member airline, but may travel on a different flight."

except...

"United Airlines' Premier Executive and Premier Executive 1K customers and US Airways' Chairman Preferred and Gold Preferred customers have access to U.S. domestic United Red Carpet Club and US Airways Club locations only when they present a ticket or boarding pass for a same-day international flight."

plus a couple of other exceptions that are irrelevant here.