They’re referencing a classic Electricity & Magnetism proof. Given an infinite sheet of uniform charge density, the electric field is constant at all distances from the sheet, which is deeply unintuitive.
I feel like I want to plot this now to build an intuition.
The situation is similar for an opaque light source (apart from the lack of atmosphere in the way, I don't think the sun would be much brighter if you were much closer to it and looking through a pinhole), but I'm not sure it applies to gamma radiation which is emitted uniformly in all directions from each point and treats most stuff as pretty transparent - unless there's some weird interference you don't get to cancel out the parts coming from different directions.
What I'm suspecting is that under a certain distance for a given finite plane it's almost constant similar to the infinite version, but outside of that distance there must be some non uniform falloff function.
A rectangle is a mess. It's easier with a circle. The approximations at short and long distance are the same, but a circle has an "easy" formula in between. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elelin.h... 1-x/sqrt(x^2+R^2) where R is the radio of the circle. Let's use R=10 to keep it simple.
For a short distance 0<x<R/10, then it's almost a constant https://www.wolframalpha.com/input?i=1-x%2Fsqr%28x%5E2%2B10%...
For a long distance, x>4R it's almost like R^2/(2*x^2) https://www.wolframalpha.com/input?i=1-x%2Fsqr%28x%5E2%2B10%...
There are some trick to add more term to the approximations to reduce the middle part where both approximations are bad, like using A+Bx or A+Bx+Cx^3 for short distance and D/x^2+E/x^4 or D/x^2+E/x^4+F/x^4 for long distance. It depends on how much you care about the precision and how many calculations you want to do.
In some particular cases like a circle or the shell of a sphere there are closed formulas for the intermediate distances. In other cases there is no nice formula.