A perhaps better explanation of this issue is that given a shared ground or indeed positive battery supply, the other circuit carrying a greater current will create a voltage change proportional to the current flowing through the shared cable as seen at the point where the two circuits split to individual. This change (lower if in positive leg, higher if in ground leg) will be very small and in the order of millivolts but the fuel gauge, as mentioned above essentially a voltmeter and a sensitive one at that, will reflect this voltage change in gauge needle movement. It follows that as the other circuit current varies so will the fuel gauge reading.
Note in such cases it's not the actual ground connection causing the issue but the shared circuit aspect.
