Here is a counter-example: let $A=(3,0)$, $B=(1,1)$ and $C=(0,3)$. Take $Y=\{A,B,C\}$. Then:
$PE=\{A,B,C\}$, so its convex hull is a triangle.
$Z$ is the same triangle.
$E$ is the edge $AB$ of that triangle.
Update: oupps, this is not a counter-example to the question, since in the question coordinates are 0/1