Conjecture on directional extension of bad points under $\Lambda$-poisedness

Let $y^1,y^2,y^3,y^4$ be interpolated points, and write $\overrightarrow{y^i y^j}$ for the vector from $y^i$ to $y^j$. A point is called bad under $\Lambda$-poisedness when it satisfies the paper's bad-point criterion for $\Lambda$-poisedness. Directional-extension conjecture. For every $i,j,k\in\{1,2,3,4\}$ with $i\neq j\neq k$, if

$$\overrightarrow{y^i y^j}=\lambda\overrightarrow{y^j y^k},$$

where $\lambda\in\mathbb{R}$ and $\lambda\neq0$, then there is at least one

$$y^5\in\{y\mid \lambda\overrightarrow{y^j y^k},\ \lambda\in\mathbb{R},\ \lambda\neq0\}$$

that is bad under $\Lambda$-poisedness. This conjecture captures the paper's observation that collinearity or strong directionality among interpolation points can extend the range of bad points substantially beyond those points; no proof or resolution is supplied.