This is not the sign of a president standing by his man.
From the White House Pool Report (i.e., one reporter traveling with the president and reporting back to the others):
Pool Report #4, 7/15/05
NORTH CAROLINA TO ANDREWS
On the tarmac in North Carolina, your pool was able to walk briefly alongside the president and ask if he still had faith in Karl Rove. The question was met with a stare straight ahead, silence and a quick brush-off motion of Bush's left hand, as if the president were Swatting away an insect.
Karl himself was more jovial on the tarmac, where when surrounded by reporters he grinned and held up the president's suit jacket, as if to say that he was a coat-holder and nothing more. The president at this point was under the hot sun in shirt sleeves signing autographs for a crowd of onlookers.
Despite his antics, Karl answered no questions, and soon trundled quickly away from your pool toward the stairs of Air Force One.
Other than that, nothing of interest happened. The president signed autographs for nearly half an hour. Air Force One took off around 2:30 p.m., and we're now airborne.
Touchdown at 3:31 p.m.
Elisabeth Bumiller
NYT