Thing is, that if two points in a circuit are actually "ground" (i.e. 0V potential) then by definition, no current can flow between these two points.
When current does flow between two arbitrary points on a circuit (that we may consider to be 'ground') this actually means that one or another of these points is actually not ground. Only one of them is. Conventional current flows from high potential to low potential.
I have had this experience working with a camera and wireless audio gear that was entirely DC powered. The 'ground loop' that was set up was only curable by cutting the ground line in the balanced line audio link back to the camera. (This only worked because the feed back to the camera was balanced). The potential difference caused the battery pinch to induce an AC (audible) signal in through the power connection - which ideally shouldn't have mattered - but it affected the wireless audio output.
A potential difference such as this would ideally not actually create anything audible, other than the fact that there was possibly a design flaw in either the power supply equipment and/or the wireless gear I was using.
I suspect that this situation is common - the undesired potential difference coupled with an equipment flaw causes the audible artifact that we detect as a 'ground loop'.