I've had them say the same thing at the small limited-hour LH Lounge at IAH (Houston Intercontinental) airport.

Despite the web site saying any Star Gold on any Star flight, and despite the Star Alliance logo with the Star Gold mention on their signage...I've always been told it's only for those on the LH flight.

I've then sort of nicely pushed the issue and they've always eventually relented and let me in even though I was on a United Domestic ticket. But I always know I'm in for a challenge there (although a few are getting to know me by now and just welcome me by name).