Thanks. What that tells me is as long as you step your gain in multiples that do not introduce rounding errors, you will see no distortion.

So the more accurate statement is that adjusting the volume on digital audio MAY cause distortion if it is done poorly.

No, the audio data will always be altered by the scaling operation (which amplification/deamplification in the digital domain really is all about). There are techniques, however, as the linked article suggests, to apply dithering to partly hide the effects of the scaling.
To explain this further, assume you have audio data in 8-bit which utilizes all the dynamics available in 8-bit. Then you have samples ranging from all ones (255) to all zeros. If you apply half volume on it, the resulting audio data would be scaled to range from 127 to 0, as if you would have removed (actually truncated) the last bit on the original audio. Two samples in the original stream that had the values say 127 (0111 1111) and 126 (0111 1110) would now have scaled down to 63 (0011 1111) and 63 (0011 1111) - that is they are indistinguishable and thus we have lost information in the process.
Dithering is a technique to overcome this. A simple kind of dithering would be the following:
Say we had two consequtive samples in the original audio data with values 127 and 127 (see bit patterns above). The scaled samples should have been 63.5 and 63.5, but this is impossible. The idea of dithering is to compensate for this by making the first value 64 and the second 63, which evens out to 63.5 and to some extent more preserves the characteristics of the original data.
But it is still not the same as the original data, right?