Yes, same here. That is most likely causing all the issues. I managed to print it fine with Slic3r 1.2.9, both Cura and Simplify3D failed, and Netfabb (both cloud and basic) could not repair the mesh. Simplify3D can flip the normals, but it still fails to slice properly after fixing. If you notice, the STL has a mesh pattern on the bottom that Slic3r turns into a solid surface, which makes this print work as a vase. If it was sliced correctly, it wouldn't work by itself :)
Still very happy with this print, though it is useless as a pencil holder in its default size, and has to be printed at least at 150% or 200% size to hold pens without tipping over. Thank you @philnelson for sharing it!