It has to do with the I(squared)t, or amp-squared seconds. ground rods are basically for lightning, and lightning is of very short duration meaning No.6 bare or insulated can with stand much much more current for a short duration than that listed in 310.16.
for example a 2 cycle fault or 0.0333 seconds, using No.8 can withstand 4791 amps. This is from Soars Book on grounding.
IEEE lists No. 6 at 684 Amps for 5 seconds, using the I x I x Sec. is 2.339e6 amps or over 2million amps for 5 seconds, or for the 2 second example 8381.4 amps for 2 cycles.