The Schubert-calculus form of the rational total reality conjecture

Let $0\le d<n$, let $t_1<t_2<\dots<t_{(n+1)(d-n)}$ be real numbers, and let $\mathbf r:\mathbb C\to\mathbb C^{d+1}$ be a rational normal curve with coordinates $r_i(t)=t^i$ for $i=0,\dots,d$. For each $i$, let $T_i$ be the osculating $(d-n)$-dimensional plane to $\mathbf r$ at $t=t_i$. Schubert-calculus interpretation. Any $(n+1)$-dimensional subspace of $\mathbb C^{d+1}$ that meets all $(n+1)(d-n)$ subspaces $T_i$ nontrivially is real. The source states this as equivalent to the rational total reality conjecture, but provides no resolution status.