It is shown that the ’new’ runaway criterion for electrons in dense gases suggested by Tarasenko and Yakovlenko (Usp. Fiz. Nauk 174 953 (2004) [Phys. Usp. 47 887 (2004)]) is actually not a criterion, and the ’upper’ curve of the U(Pd) dependence does not exist. Only the Z-shaped segment of U(Pd) in the region of small Pd, known for helium since the early 1930s, agrees with the reality. The decrease in the ionization coefficient with E/P increasing and the existence of Pd_min for helium have been known since the same time. Doubt is cast upon the ’record’ runaway-electron currents at P = 1 atm. The acceleration mechanism suggested in the above article has been known for a long time, and the interpretation of the ’record’ runaway-electron currents on this basis is the result of fitting the data to the formula that implies the lack of electron multiplication but is ’understood’ by Tarasenko and Yakovlenko as a runaway criterion. Nothing new has been added to the mechanism of volumetric discharge formation, but mistakes have been made.