Multiple _separate_ grounding electrodes that are not bonded together might be considered a case of 'too many grounds'. For example if the telephone service has a ground rod for its lightning protection, and this ground rod is not bonded to the electrical grounding electrode system.
In this situation, any 'step potential' (voltage difference from one patch of soil to another) could be picked up by the different grounding electrodes and show up internally where the two systems are in close proximity; eg. ground potential from a nearby lightning strike could cause current to flow 'in' via one grounding electrode, through your telephone equipment, and 'out' via the other grounding electrode.
-Jon
