The survey was indeed conducted by the Gallup organization SECRETLY in mid-October 2001. The survey was commissioned by the Saudi regime's intelligence agency Istikhabart. Gallup denies the story because it does not want to lose its lucrative Saudi and other Muslim clients. But it was reported in the media after it was leaked by Saudi regime officials and by U.S. diplomats in Saudi Arabia.
Here is one of the journalists, Dilip Hiro, who wrote about the poll in the March 11, 2002 edition of The Nation, a leftwing magazine:
A secret survey in mid-October by the kingdom's intelligence agency, Istikhabart, showed that 95 percent of educated Saudis in the 25-to-41 age group supported "bin Laden's cause." Given this sociopolitical fact, it seems unlikely that the regime in Riyadh can continue its tight military links with Washington. The writing is on the wall. "Since September 11 America has lost the Saudi people," said Dr. Abdulrahman al-Zamil, chairman of the al-Zamil business group. "America tried to convince people that they are here to protect the [Saudi] regime, and that is total garbage. Their presence is a liability to the Saudi government." The airing of such a view by an affluent businessman, who is also a member of the consultative council appointed by the monarch, could have happened only with the connivance of the royal family.