Conjecture on level curves of even bent functions

Let $f:GF(p)^n\to GF(p)$ be an even bent function with $p>2$ and $f(0)=0$. For each value of $f$, its level curve is the corresponding level set; assume these level curves give rise to a weighted partial difference set in the sense of the cited remark. Conjecture on level curves. If the level curves of $f$ give rise to a weighted partial difference set, then $f$ is homogeneous and weakly regular.

The claim proposes a converse to the known construction for homogeneous weakly regular bent functions, extending that property to characterize the functions whose level curves produce weighted partial difference sets. The supplied text gives no resolution, so the conjecture remains open.