Let $X$ be a complex variety with a good stratification $S$ and consider the category $Perv_S(X)$ of sheaves perverse with respect to the given stratification (with middle perversity) lying in $D^b_S(X,k)$, where $k$ is a field. By good I mean that the derived pushforward from any stratum of a complex with constructible cohomology is constructible with respect to the same stratification.

I want to compute the Yoneda-$\text{Ext}$ groups for arbitrary perverse sheaves $F,G\in Perv_S(X)$. It is true that $\text{Ext}^i_{Perv_S(X)}(F,G)=\text{Hom}^i_{D^b_S(X,k)}(F,G)$ for $i=0,1$, since this is true for the heart of any $t$-structure. I know that this holds for $i>1$ if we do not fix a stratification, since the bounded derived category of $Perv(X)$ is equivalent to $D^b_c(X,k).$ Is the same result true for a fixed good stratification, or maybe with some additional hypotheses?

There is a paper on this topic by Beilinson: "On the derived category of perverse sheaves", where he idendtifies the bounded derived category of $Perv(X)$ with $D^b_c(X,k)$ (and also in a lot of other settings), and then writes:

a) The corresponding statement for the category of sheaves lisse along a fixed stratification is usually false,

but I am not sure whether this refers only to the $l$-adic case.