Extension conjecture for neutral fibre functors on hyperbolic curves

Let $k$ be a field of characteristic $0$, let $U$ be a hyperbolic curve over $k$, and let $V\subset U$ be an open subscheme defined over $k$. Write ${\sf Fib}_k(U)$ and ${\sf Fib}_k(V)$ for the sets of neutral fibre functors.

Extension conjecture. Every $\rho\in{\sf Fib}_k(U)$ extends to a functor in ${\sf Fib}_k(V)$.

The paper presents this as an immediate consequence suggested by the section conjecture: geometric and tangential fibre functors should remain realizable after passing to the open curve $V$. The supplied source gives no resolution evidence.