Consistency of distinct selection principles for tau-covers

Let $X$ be a topological space. Write {\sf S}_1(\{\mathcal O_n\}_{n\in\mathbb{N}),\mathrm{T}) for the property that, from every sequence of covers $\mathcal O_n$ of the relevant type, one can select a single member from each cover so that the selected family belongs to $\mathrm{T}$. Write ${\sf S}_1(\Omega,\mathrm{T})$ for the corresponding selection property for sequences of open $\omega$-covers, where $\mathrm{T}$ is the collection of open $\tau$-covers. Consistency conjecture for tau-covers. It is consistent that

$${\sf S}_1(\{\mathcal O_n\}_{n\in\mathbb{N}},\mathrm{T})\neq{\sf S}_1(\Omega,\mathrm{T}).$$

The paper notes that ${\sf S}_1(\Omega,\mathrm{T})$ implies Rothberger's property ${\sf S}_1(\mathcal O,\mathcal O)$, so consistency of Borel's conjecture prevents replacing “consistent” by “provable.” The claim is presented only as a guess, and no resolution of the consistency statement is supplied.