Not true. I have personally seen copies of some of the correspondence between Rav Soloveitchik z’tz’l and Rav Lieberman z’tz’l from the 1950s when they were trying to set up a joint beit din across Orthodoxy and the Conservative movement. Interestingly, it was the Conservatives who backed out. The Rav would never have agreed to serve on a beit din with an apikorus!
I never was a fan of the Rav.
In any event, I’m not sure what that story is supposed to prove. I’m sure the Rav didn’t think that conservative judaism is legitimate.