Ground is an unfortunately vague term which should not be used unqualified in an audio discussions. In audio designs there are generally two grounds to consider "0V analogue" and "chassis". 0V analogue is the audio signal reference and is typically the trace that is made into a ground plane of a PCB. Minimizing its impedance is a good thing in general however, in all but the simplest of designs, it is only possible for this ground plane to cover a significant area of one side of the board (because all the other connections are on the other side). Flooding the opposite side and stitching it to the ground plane with vias may provide little additional lowering of impedance. In addition, if there are any high impedance signal traces (as there are in this design) it is important not to add any unnecessary capacitance to ground which is exactly what a ground plane may do.
"chassis" is the metalwork of the enclosure. Its purpose is to route interference away from 0V analogue and straight to safety earth. 0V analogue is also connected, at one point only, to safety earth. You therefore need to take care that mounting holes connected to 0V analogue do not accidentally create an additional connection between 0V and safety ground.
Cheers
Ian