thats correct, absolute permeability is property of rock. No matter what gas you use for measurement in lab, Klinkenberg corrected value should give the same absolute permeability value.
This is important when you perform relative permeability measurement, because some procedures use value of permeability of a observed fluid when 100% flow of that fluid occurs. But this value is not the same permeability value as absolute - this only the maximum effective permeability that can be obtained from a two (or three) phase system.
Then, you should be sure if the relative permeability (or back calculated effective perm) is obtained as curve calculated from absolute permeability, maximum permeability, and also is the kr curve normalized.