Well they would, wouldn't they? But the US press account seems determined to make this a dispute between the US and Pakistani governments when in reality it is a dispute between the democratically elected politicians and anti-democratic factions in the military.
Neither Bin Laden nor the Taleban were ever popular in Pakistan. Musharraf, their main supporter in Pakistan was never popular either, he seized power in a coup and lost it the first time there was a democratic election.
The reason the Pakistani government needs to tread cautiously and appear to resist certain types of US pressure is not fear of domestic Taleban/Al Qaeda supporters. Even though they do exist, they never voted for Benhazir Bhutto's party anyway. The reason they have to be cautious is the risk of a military coup.
So it probably suits the Pakistani government to appear to be under pressure from the US to perform a purge of the military. It gives them a pretext to 'reluctantly' do what they would like to in any case. Just as Pakistan has to officially appear affronted at the invasion of its sovereignty in the killing of Bin Laden while being rather glad he is eliminated. The Taleban imposed a far more humiliating infringement on Pakistani sovereignty when they occupied and effectively rulled the Swatt valley for a period.