Hard to see how sanding the top surface can remove stain between the boards.

Stain can also penetrate quite deeply into the end grain of the timber and come to the surface several inches from the ends of the boards. Can't be sanded off because it's in there like the writing in a stick of seaside rock. Likewise knots and other defects may remain stained.

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That would involve an enorous amount of work, you would need to take off the skirtings, which would almost certainly damage your decorating. The boards would not necessarily be smooth on the underside, and taking them up and removing the nails can seriously damage the boards. Plus some boards may well run under internal walls, furthermore if you used a lot of stain as CWatters said it may well have gone through the boards paricularly near knots and at the edges.

I'd pick a corner of the room that has furniture on it and give it a light sand, it may well look very patchy where the stain has followeed the grain, in which case i would leave it alone and live with it. If it lightens it to an acceptable finish then you could sand down the rest of the floor.