Let $X$ be a smooth affine scheme over a finite field $k$. Denote its Witt ring by $W(k)$, and the fraction field of its Witt ring by $K$. Let $F\text{-Isoc}(X)$ denote the category of convergent $F$-isocrystals on $X$. If $X_K$ is a smooth lift of $X$, then there is a forgetful functor $F\text{-Isoc}(X)\longrightarrow \operatorname{VIC}(X_K)$, with values in the category of vector bundles with an integrable connection.

A $K$-rational point $b$ of $X_K$ induces a fibre functor on $\operatorname{VIC}(X_K)$. This works by sending $(\mathcal{E},\nabla)$ to $\mathcal{E}_b$. When people speak about fibre functors for the category $F\text{-Isoc}(X)$, they typically pick $b$ to be a point of the special fibre, and identify the value of the associated fibre functor on an object $(\mathcal{E},\nabla,\Phi)\in F\text{-Isoc}(X)$ to $\mathopen]b\mathclose[^*\mathcal{E}$.

What is the reasoning behind these different conventions? Is it still possible to neutralize the Tannakian category $F\text{-Isoc}(X)$ using a $K$-rational point as in $\operatorname{VIC}(X_K)$? I suspect this is a stylistic preference that has to do with the fact that locally constant sheaves trivialize on contractible neighborhoods (such as a residue disk).