Most of the compensation is done in the optics of the scope, not on the pixels in the acquired image. In short, a laser is aimed at the sky and imaged, and the mirror itself (usually the secondary) is bent to compensate for the distortion to make the image of the laser as sharp as possible. Since you're aiming the scope at the same portion of the sky as the laser, the compensation works for the stars in that area of the sky. This happens hundreds of times a second (the atmosphere has this annoying habit of being turbulent). It's pretty amazing technology, but to say that it's "photoshopping" is like saying that focusing a camera is "photoshopping."
Yes, the image goes through some noise cleanup, but so does the image from your DSLR, your point-and-shoot or even your cellphone cam.