I have heard that too, and asked the same question without adequate answer. The implication is that the PEN is of too high a resistance and the voltage drop in it too severe, but the Ra of the earth rod is somehow low enough to provide an effective parallel path thereby mitigating the voltage drop. Since a typical customer's earth electrode Ra is 100 - 1000 times higher than a typical Ze, the reduction of voltage drop it can provide will be in the order of 0.1 - 1% (of the variation, not the supply voltage). Noting re. voltage drop that in a US domestic installation the PEN is normally a centre conductor between split-phase lines.
If an electrode of vanishingly low Ra were provided, the overall Zpn would be reduced and the voltage drop mitigated, but only because a significant fraction of the load current (and possibly other peoples' load currents) would return via the electrode. We accept that these currents do flow, hence the bonding requirements for TN-C-S, but surely no regs would sanction relying on the electrode as part of the load circuit absent a solid PEN connection, (other than for a SWER supply.)