The far-field concept is related to ensure an almost plane wave is illuminating the antenna under test by the source antenna.
For better understanding, in the picture attached, ΔФ = (ΠD^2)/(4λR)
If the ΔФ = Π/8 or 22.5° then we get the well-known far-field distance R = (2D^2)/λ.
The 22.5° is the acceptable allowable phase variation to give the required accuracy in measuring the antenna under test gain and pattern.
However, for the parabolic reflector antenna case due to its construction, the waves leaving the antenna are almost parallel one to each other, giving a nearly plane wave front.
So in this situation, this might be the reason that some people may chose smaller distance for far-field, other than (2D^2)/λ.