I control the variables I want to control like ISO (noise) and aperture (depth of field) and monitor the shutter speed to make sure it is in the range I want.
What is the difference between reading the meter to set manual exposure vs setting either shutter or aperture? Let's assume you set ISO; no auto ISO. If you set exposure manually you have to choose a preferred blur (shutter speed) or depth of field (aperture). The last variable is determined based on the meter's suggestion and the amount you want to over or underexpose based on your understanding of the meter's guess vs your desired effect.
Whew! In the end, you have to understand your camera's metering system. I have a reasonable feel for when the camera is going to get it 'wrong'.
Is it 'manual exposure' if I get my exposure from an area that I know will get it right, lock exposure, recompose, and shoot? If Yes, then the next statement is a bit off.
I shoot almost everything in aperture priority. If the situation is static I'll dial in compensation. In those cases I know the variation between my vision and the camera's guess at metering. For example I often dial in exposure compensation for snow fields, sand beaches, certain night time shooting, and my artistic vision of high or low key. The D100 was a bit off on snow, the D3S does a heck of a lot better.
Manual mode is used where the lighting changes as Brian described with headlights that move and cause the camera to go wild. I go straight to manual at that point and get the photo I want.
Manual is also my method of choice when I want to play with the mood and I start shooting over and under exposed, exposed for one item in the shot . . . . Let's face it, a lot of times at this point I'm guessing and trying to figure out what I want.
I shoot sports and journalism stuff recently. I used aperture for landscapes too because I'm most concerned with depth of field.
Manual is required for use of tilt and shift on the PC-E lenses. I love those lenses. Yes they are slow but manual everything changes the photographic session.
To directly answer your questions. "real photographers only shoot in manual" Bull stuff! Real photographers control their cameras and make it take the photo the photographer sees.
Yes, with digital you can tweak. Just like film you can push, pull, dodge, burn, etc. Just like film the further you are off in camera the more labor later and the more risk you'll see grain (noise) or bad color, or simply not have the information at all.
Yes, I generally just let the camera do its thing and tweak later as required. BUT / HOWEVER . . . I do it as an educated choice. I let it choose anything I want it to choose. See exposure compensation, metering to the side and recomposing, controlling depth of field, and all that above.