Why are BRDF and the lighting uncorrelated?
When rendering an image you are trying to find the outgoing light from a point into the camera $L(x \rightarrow \Theta$).

To do this you solve "The rendering equation", which means you integrate the product of the brdf and the incoming light for every incoming direction.

$$L(x\rightarrow\Theta )=\int_\Omega f_r(x, \omega\rightarrow\Theta)\cdot L(x\leftarrow\omega)d\omega$$

Since you don't have the outgoing light you cannot use the definition of the brdf to calculate it.

$$f_r(x,\omega\rightarrow\Theta )=\frac{L(x\rightarrow\Theta)}{E(x\leftarrow\omega)}$$

Instead, you use a formula to compute $f_r(x,\omega\rightarrow\Theta )$ and some operation to find the incoming light $L(x\leftarrow\omega)$ (a raytrace, a env map sample, etc.), and use those to compute the outgoing light $L(x\rightarrow\Theta)$.

These two calculations are usually done in a completely separate way. So there is no way the incoming light can effect the brdf in any way.