The natural assumption would be that they do. But if you think about it a little deeper, then maybe they don't. Starting with my four-year term in the US Air Force in 1961, I have become increasingly skeptical about the pronouncements of the US government.
I heard a “conservative commentator” on TV say that if we left Iraq now, it might just mean putting Saddam back in power. That turned my suspicions mind in a new direction. If Saddam were dead or captured, that would be one less reason to leave Iraq. The same goes for Osama and Afghanistan.
A lot of people don't want to end the war in Iraq, and some of those people seem to be the ones that are controlling the media and the government.
But if Saddam and Osama are in US jails, that would explain why we only get audiotapes with no video. It would be very difficult to produce a convincing video from a prison, but audio is another matter. The thought that the CIA might be producing the Saddam and Osama show and providing tapes to Aljazeera is at least an interesting flight of fancy.
The Neocons could be stringing us all along with occasional tapes that “proved” that Saddam and Osama were still alive so they could have a perpetual emergency and perpetual emergency powers.
I've heard a lot of comment about the content of the tapes. Why didn't Osama make a video and hold up a newspaper to verify he is still alive. It's hard to understand why a wealthy and powerful man with so many friends wouldn't be able to come up with a $400 video camera. Why would a person who once had a very slick media operation suddenly be so limited in communications bandwidth? Why didn't he mention this or that event? But if he were in prison being in-terror-gated, it might be difficult to control exactly what he said. His intonation might be a trifle strange, he might sound weak or sick. The bug in his cell or interrogation chamber might not have the best fidelity.
CIA certainly wouldn't want pictures. They wouldn't want any kind of effective, modern, high-bandwidth communication. They would just want enough “proof” to keep skepticism to a minimum. They would also like to keep Osama and Saddam from becoming martyrs.
The drug war couldn't exist without a substantial trade in drugs. Perhaps the drug warriors don't really want to eliminate drugs, they just want the drug war graft. The war on terror would be a dead letter without the verified existence of terrorists.