The arrival of Republican media strategist Mike Murphy (search) in Arnold Schwarzenegger's campaign reunites top advisers to Bob Dole's 1996 run for the White House, offering fresh proof, GOP strategists say, that Schwarzenegger's bid for governor is not taking cues from the Bush White House.

Murphy will join top Schwarzenegger political and media strategist Don Sipple (search), who replaced George Gorton (search). The two will form the campaign's political and media brain trust, Republican sources told Fox News.

Sipple and Murphy did the same for Dole's 1996 campaign and Sipple, say several sources, had been pushing for Murphy's hiring for at least two weeks.

"They are old friends and they are used to working with each other," said GOP strategist Kevin Spillane. "Hopefully, the relationship will be complementary."

Murphy had been planning to run the media campaign for former Los Angeles Mayor Dick Riordan (search) before Schwarzenegger's surprising entry quashed Riordan's bid.

Murphy handled media for GOP Sen. John McCain's presidential campaign in 2000. Murphy persuaded McCain to run a commercial before the South Carolina GOP primary saying then-Gov. George W. Bush was no more trustworthy than President Clinton.

"I guess it was bound to happen. Gov. Bush's campaign is getting desperate with a negative ad about me," the Murphy-approved spot had McCain saying to the camera. "His ad twists the truth like Clinton. We're all pretty tired of that."

The spot infuriated top Bush political adviser, Karl Rove (search), and the ad backfired on McCain, who then pulled it. Bush went on to win South Carolina. Rove and Murphy have had a testy relationship ever since.

"I think it's fair to say that Murphy's arrival in the Schwarzenegger campaign reinforces the point that the White House is not involved," Spillane said.

Interestingly, Sipple handled media for Bush's campaign and plotted Bush's response to McCain's attack ad, which was to decry his use of such tactics.

The Schwarzenegger campaign declined to discuss Murphy's hiring.