The linear-general-position projection conjecture

Let $Z\subset\mathbb P^3$ be a set of at least $5$ points in linear general position, meaning that no $3$ points of $Z$ are collinear and no $4$ points are coplanar. Projection conjecture. The general projection of $Z$ to a plane is not a complete intersection. This conjecture asserts that complete-intersection projections are necessarily associated with special linear configurations, such as grids, rather than sets in linear general position. The source provides motivation from its analysis of grids and proves the corresponding classification for non-degenerate sets of $9$ points whose general projection is a complete intersection of cubics, but does not state a resolution of the conjecture.