The jihadists are actually hoping for large-scale U.S. military activity on Pakistani soil because they desperately want to broaden the scope of their insurgency from one currently being waged by a religious ideological minority to one of a nationalistic flavor bringing in participation from more mainstream cross-sections of Pakistan.
"Ideological minority" is right.
Far from being a conundrum, Stratfor's read on things actually highlights why chest-forward Americans (including Obama liberals who want to go into Pakistan as a way to right Bush's blunder in Iraq) are way off base when they haul out the "Pakistan 2008=Afghanistan 2001" analogy.
In 2001, when Al Qaeda had its pretty set up in Afghanistan, Afghanistan was actually under the Taliban's control. Pakistan, while definitely a bit of a mess, has a secular-liberal party with a majority in parliament (parliament!), a mainstream conservative religious party in the minority, and streets flooded with activists rallying around the country's well-established secular legal system.
Basically, there are democratic institutions (and an engaged population) in play in Pakistan that Americans can support. Doing so will isolate and unplug the losers in the hinterlands.