Klyosov correctly criticizes the authors for using the evolutionary mutation rate:
However, it should be noted that the +/- 130ybp limit around the estimated age of Cohanim J-P58 is too small, and gives the false impression of great confidence in the age estimate, which is not really warranted by Y-STR markers.
A common ancestor of all 99 Cohanim lived 1,075 ± 130 ybp, and this timing is reproducible for 9-, 32412-, 17-, 22- and 67-marker haplotypes. A much higher values of 3,190 ± 1,090 and 3,000 ± 1,500 ybp were obtained in the cited paper (Hammer et al. 2009) using incorrect methods and incorrect mutation rates.
Please note that Klyosov uses both a mutation-counting "linear" method, as well as a "logarithmic" method which relates age to the fraction of inferred ancestral ("base") haplotypes in a collection; the "linear" method produces age estimates of comparable error as the more commonly used ASD/variance methods, but the "logarithmic" method produces sufficiently worse (larger confidence intervals) estimates. You can easily modify the Y-chromosome Microsatellite Genealogy Simulator to test the performance of Klyosov's methods.
In conclusion: Klyosov is right to criticize Hammer et al. for using the evolutionary mutation rate. However, his methods do not warrant the strong conclusion that Cohanim J-P58's share a common origin in the last 1,000 years. See my own post on the Hammer et al. paper for my thoughts on the matter.