Let $S$ be a scheme, $G$ a smooth affine group scheme over $S$, and $X$ an $S$-scheme with a ($S$-linear) $G$-action $G\times X\rightarrow X$.

Let $h_X$, $h_G$ be the representable sheaves on the small etale site $S_{et}$ associated to $X,G$ respectively. Suppose $h_X$ is a torsor under $h_G$. Must $X$ be a $G$-torsor?

I'm happy to assume $G$ reductive if it helps.