It's not transparency or dodging but rather a realization that many operations are now run by joint task forces drawn from many varied units across the military. Furthermore, the world has already recognized that we are operating armed drones in other countries, so running it as a dark operation under CIA auspices did not make sense anymore.
The failure of Operation Eagle Claw was found to be a result of military branches not training, working, or coordinating with each other adequately. As a result, each branch of the armed forces "detached" their tier one units (Delta Force, SEAL, Ranger, etc.) into a central commandâ"SOCOMâ"in 1987.
However, in theory, the military operatives of SOCOM were not deniable assets and had to report to civilian oversight. To take care of intelligence functions that require deniability or transparency, the CIA has its own operations group called the Special Activities Division and in particular, the Special Operation Groups within SAD. These guys were at the tip of the spear in the Afghan War, but there is always the case of Raymond Allen Davis, a "diplomat" who shot two guys in Pakistan through his windshield, then walked over to take pictures, and was then arrested.
CIA dominance of the armed drones program was a historical artifact. CIA ran the first armed Predator, call sign Wildfire, in Afghanistan because it couldn't get the Air Force or Army to strike fast enough when unarmed CIA drones provided actionable intelligence. The Air Force declined to co-fund the program, so CIA took the lead. It helped that CIA was also able to operate in denied areas to obtain targeting information for drones in countries such as Somalia, Afghanistan, Pakistan, and Yemen. The fact that CIA drones were "off the books" provided a fig leaf for operations in Pakistan, which was a nominal American ally.
However, the world now knows that the US is running around blowing shit up all around the world. The difference between CIA paramilitaries and U.S. military men is not that important in the eyes of the world. Thus, keeping drones a dark program under CIA really stops making sense from an intelligence standpoint.
This culminated in the Bin Laden raid, which drew upon an alphabet soup of military and intelligence personnel. Originally, the shooters were going to be CIA SOG operators who could be denied if the operation went side ways. However, that was quickly revised to take a dream team of shooters from DEVGRU with instructions to shoot their way out of Pakistan if necessary. A second Chinook of shooters was added to the mission to provide the firepower necessary to smash Pakistani military and police forces who may have tried to stop the operators from leaving. In contrast, CIA operatives in the past were disavowed and left to rot. The best example I could think of were the three CIA operatives who were arrested in Cuba in the sixties. They spent three years in a Cuban jail without admitting their CIA affiliation under interrogation (duh, we're just tourists with sensitive spy equipment bugging a newly-built embassy, stop hitting me) until they were exchanged for Cuban spies arrested in New York.
The shooters on the Bin Laden raid were operators from the Navy SEAL Team 6, directed by targeters at the CIA, with an Air Force RQ-170 Sentinel overhead providing real-time video to leaders, Army CENTRA SPIKE/GRAY FOX operatives providing signals intelligence, NSA providing intel, and the National Geospatial-Intelligence Agency providing detailed three-dimensional measurements of the Bin Laden compound and ground penetrating imaging to show that there were no escape tunnels under the compound. CIA also put eyes on the ground in advance of the raid, trying to get a glimpse of Bin Laden, and also sent a doctor to try to draw blood from the residents of the compound to try and match it with the DNA of Bin Laden's sister. Oh, yeah, and when the stealth choppers flew in that night, the power to the area immediately around the compound went down as a result of CIA operations.
I think shifting the drone program to the military is meant to change it to a "white" program that is under civilian review. Whether or not that changes how drones are used is anyone's guess. It's also a no brainer that CIA will keep some drones for its own use.