While it's less clear that Pakistan actively sponsored al-Qaida, it certainly wouldn't surprise me if they tolerated it and gave medical attention to Osama at a non-military hospital during that period.
Osama has enough money to buy and equip his own field hospital anywhere he wants. I can't imagine he's dumb enough to seek treatment at a legitimate hospital in Pakistan today. A $50 million bounty on your head would make anyone nervous.
There are still factions in the Paki military who are involved with AQ to this day. Something else to keep in mind.....the Pakis just arrested two doctors for aiding the Al Qaeda terror network inside Pakistan.