Earth moves - that's how you get the next shot without repositioning the telescope.
This time-lapse probably better visualizes it: https://www.youtube.com/watch?v=wFpeM3fxJoQ
Sure, but the nebulae also move along with the stars. The questions is how one can subtract the stars without also subtracting the nebulae. (I'm assuming different filters and/or a database of known star positions)
As the Earth rotates over the course of the night, the background stars and nebulae move as a single unit, no?
Maybe for some close stars parallax might work to remove them over the course of half a year. But no way could the Earth's rotation during a single night move background stars out of a nebulae.