Without air to scatter sunlight, the sky around the sun's disk is just as dark as it is in any other direction. However, a camera (or the human eye) will automatically "stop down" if dazzled by a bright light source in the field of view, making the much fainter stars appear to disappear. But they are still there. If you simply step in the shade, the stars will reappear as soon as your eyes adjust.

As an example, an astronaut working outside his ship's hull on the sunny side of the spaceraft will be exposed to sunlight from the sun and reflected off the ship itself. But the moment he moves over to the shadow side, not only will the stars pop out in all their glory, but his surroundings will be plunged into darkness and he'll have to flip on his helmet lamp to see what he's doing. Likewise, a crewman inside the hull would be almost blinded if he looked out a sunward facing port, but would see the Milky Way, Zodiacal Light and Gegenschein easily by looking out a window on the opposite side of the ship. And don't forget, the earth itself is an extremely bright source of sunlight reflecting off the cloud tops and icecaps.

Which all leads to a related question: on their time off, when not looking at the earth below them, do space travelers spend any time looking at the stars? Or are the spacecraft windows clear enough (and the cabin lighting dimmable) to let them do that? It's always been my fantasy to see the night sky without having the atmosphere get in my way. Can you visualize the Sagittarius Milky Way with nothing but a few millimeters of clear glass between you and it?