But then Assad, a pragmatist who understood the West, had long played an oscillating game with al-Qaeda, partly to keep one step ahead of Western pressure on his regime.
Even before the Arab Spring began, the same cry went up from Egypt, Libya - and Damascus: "Choose us, or the jihadis". Each beleaguered government alternately persecuted and engaged with Islamism, as pragmatism dictated.
But that reflected a bigger truth: jihadism had flourished under all three regimes, with Libyans, Egyptians and Syrians prominent in al-Qaeda.
Ayman al-Zawahiri, the Egyptian who took over from bin Laden, had been released from prison by then-President Hosni Mubarak. Abu Khaled is now his personal envoy to the Syrian jihad.
Western intelligence agencies have played their own games, of course, but in the midst of the Arab Spring's sea of change have no wish to see them revived: hence their determination, as revealed publicly now, to refuse Assad's kind offer to "resume co-operation".
It is hard in any case to know what such co-operation would entail. Allies of the West, like Turkey, could cut off the rebels' supply lines - but the rebels they are supporting are the very brigades now fighting al-Qaeda's front, the Islamic State of Iraq and al-Shams (Isis). It is being supplied from its bases in Iraq.
And what would Syria offer in return? The days of rendition of terrorist suspects are over, and the regime seems unlikely to regain control of parts of the north held by al-Qaeda, with or without Western assistance.
Instead, these "Western officials" think that only Syria's Sunni majority can defeat al-Qaeda. And they are still demanding Assad go as part of the bargain.