The "controlling agency" can clear you through restricted areas, but not prohibited areas.
The "controlling agency" CAN clear you into a prohibited area.
The controlling agency is the government agency who is responsible for useing that airspace. Millitary range controll, the USSS, NASA, ect. ATC does not manage this function, they mearly are the messager.
A hadfull of civilian operators are allowed into some prohibited areas, for very specific reasons. However you are just wasting your breath asking. Since all P areas are national security related, you would need a VERY good reason for asking, and it would probably be denied anyway.
If you can come up with a good enough reason to fly you 152 over the Washington Mall, and you can get the director of the Secret Service to agree to it, ATC will let you.