It's about the general method they are using.I don't see where in that paper you are referring to.. They seem to be pretty focused on just axial and weyl gauges
They fix the temporal gauge.
They construct a unitary operator fixing a second, residual gauge symmetry respecting the temporal gauge.
They show that in the physical Hilbert space both gauge conditions are satisfied (they use implicitly Dirac's constraint quantization for first-class constraints)
Their method applies to all gauges which can be written as "temporal gauge + physical gauge".
So the idea is quite general, even if the gauge-fixing operators are different. Unfortunately they do not discuss Gribov ambiguities.