I agree that you could design a shutter and a CCD (light sensor) that's 360 degrees, but I don't think you can make a lens in that shape. That's why people just use the current lens and point it around a circle.

There are a couple ways to do a 360 camera.

Google does it with a number of cameras around the vehicle, joined in software.

For a static image, they may use an almost standard camera on a rotary mount, which takes a series of pictures.

Lastly, there is a one shot optical system, which the lens points up and a reflective cone will refelct the image into the camera.