With some software packages you can specify a line and they will run cross sections at a nominated interval cross your surface at that direction, and calculate a volume that way, regardless of the shape of your surface. Or you can cut your surface into horizontal sections and get a volume that way. If you specify a close enough interval (1m is more that good enough) the end area and composite volumes calculates are surprisingly close, agreeing with a couple of cubic meters or better than 0.1%. Because the calculation approaches are fundamentally different, it is a useful check as to whether the software is getting a correct volume.
As Laurie said, the reliability of the surveyed surface is what ultimately determines the accuracy of the volume.
With the general bugginess of Civil3D I honestly wish there was an alternative volume calculation method included. I have exported TIN surfaces to other software packages though and arrived at very similar volumes every time, in case anybody wants to know.