Does ground effect scale 1:1 with wingpsan?
It's most definitely not urban legend. However, it also does not scale 1-1 with wingspan. Rather, it scales nonlinearly with above ground height to span ratio ($h/b$). The simplest analytical prediction for ground effect can be derived from potential theory and the circulation theory of lift. 

We know that the wing can be modeled as lifting line consisting of a line of vortex bound to the wing and trailing vortices that look like horseshoes. The trailing vortices induce downwash on the wing and everywhere else. But what about at the ground directly underneath the wing? Due to the tangency boundary condition of non-viscous flow, induced downwash must necessarily be zero everywhere on the ground.

Within the context of circulation theory of lift, the only way we can achieve this is if we have a mirror wing underneath the ground with the ground plane being the plane of symmetry, like this:



Since the image wing is exactly inverted, it produces upwash that reduces the overall downwash on the real wing. In the super simplified case of a single horseshoe vortex (which is incorrect), after some maths, the induced downwash at the wing root is now:

$$w_i=-\frac{\Gamma}{\pi b}\frac{16(\frac{h}{b})^2}{1+16(\frac{h}{b})^2}=w_{i_\infty}\frac{16(\frac{h}{b})^2}{1+16(\frac{h}{b})^2}$$

where $w_{i_\infty}$ is the downwash induced without the ground image (i.e. free-air). Turns out the latter factor is an ok approximation of total reduction of induced drag in ground effect as well. As you can see, at half wing span away from the ground, we have 80% of the free-air induced drag; at one full wing span away, we are at 94%. The effect falls away quickly.

You can read this MIT lecture on ground effect (from which I've taken the above diagram) for the derivation of the simplified ground effect prediction. More precise ground effect accounting can be found in references such as Raymer and ESDU Item 72023.