without parskip:
parskip=half:
\documentclass[parskip=half]{scrartcl}
\usepackage{blindtext}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{thmtools}
\usepackage[framemethod=TikZ]{mdframed}
\colorlet{shadecolor}{gray!25}
\newmdtheoremenv[
innerlinewidth=0pt,middlelinewidth=0pt,
outerlinecolor=shadecolor,outerlinewidth=3pt,
skipabove=\topskip,skipbelow=\topskip,
]{example}{Example}
\begin{document}
\begin{example}
\blindtext
\end{example}
\end{document}