Directional dichotomy conjecture for sets of size p in finite affine 3-space

Let $A\subseteq\mathbb{F}_p^3$ be a set with $|A|=p$. A determined direction is a direction of a line passing through at least two points of $A$. Directional dichotomy for sets of size $p$. Either $A$ is contained in a plane, or $A$ determines at least $p+1$ directions, possibly at least $p+2$ directions. The source explicitly says that it is not yet known whether this statement is true or false, and notes that the stronger $p+2$ alternative is the version used in combination with the strong cylinder conjecture.