The walls of the canyon are mostly cut into horizontal rock layers of Paleozoic age (green in Figure 1, above).
There is an angular unconformity at the bottom of the Paleozoic layers.
The ICR's Grand Canyon Dating Project does not strike a telling blow against the reliability of isochron dating.
The problem is not the age itself but rather Austin's sleight-of-hand in trying to pass off the result as necessarily the age of the flows rather than a minimum age of their source.
As discussed above, whole-rock samples of multiple flows yields the time since their common source was isotopically homogeneous.
It also be the age of the flows, but it does not have to be.
The "type" of rock is not sufficient to establish the samples being cogenetic.
Since the stratigraphic evidence indicates that the flows did not all occur at the same time, the case could only be made by other isotopic analysis such as taking internal isochrons of the individual flows.