This is what technical support had to offer:
"After consulting with my colleagues in development, the behavior you are experiencing is the expected behavior. The STL format comprises a collection of triangles that make up the boundary of the CAD model and the PDE Toolbox reconstructs the Face/Edge/Vertex topology from that data. Unlike an IGES or STEP import where the topology is fully preserved, the reconstruction from STL is imprecise resulting in the loss of edges and merging of adjacent faces."
Two Points:
1: The PDE Toolbox does not allow IGES or STEP file imports.
2: I have never run into a similar issue with another program (ANSYS, COMSOL, Meshing software, etc).
From the sounds of it they do not plan to fix the issue as it is working just fine in their opinion. Best of luck with a real solution.