Assuming the original source is a point source, then
the relevant distance is
-- from the source to the mirror
*plus*
-- from the mirror to the detector.
To say the same thing the other way, if they imagine
the front face of the mirror to be a point source,
they've got the wrong abscissa. By a lot.
This would explain the result. As the jocular saying goes:
"To first order, everything is linear."
(That's not strictly true, but it's kinda mostly usually
true.)
In particular, if you have a square law (y=x²) and you
throw away most of x and look only at Δx, then y is (to
first order) a linear function of Δx.