On June 11, California Governor Arnold Schwarzenegger said he could not have won a semi-closed Republican gubernatorial primary. See this story. Actually, according to exit polls in the special gubernatorial election of October 2003, 74% of registered Republicans voted for him in that special election.
In a related vein, supporters of Proposition 14 said during the campaign, over and over, that Republican primaries in California always result in victories for extreme conservatives. However, in all the contested Republican statewide primaries this year, with a semi-closed system, the more conservative candidate (among those who had big campaigns) lost in each instance. Steve Poizner lost for Governor, Sam Aanestad lost for Lieutenant Governor, Orly Taitz lost for Secretary of State, Tom Harman lost for Attorney General, and Chuck Devore lost for U.S. Senator.