However it doesn't do anything to modify or simplify the object.  The Pro version has a "Refine Mesh" option, which appears to do a triangle reduction, but I can't verify that since I don't have the Pro version of the NetFabb.

Again, this is what MeshLab does best.  It has the means to simplify the mesh.  So if you need to reduce the number of traingles in a mesh, load the STL file in MeshLab, then from the filter menu select Remeshing, Simplification & Reconstruction / Quadratic Edge Collapse.  from the PopUp menu select the desired number of face (by default it's half the current number), and click apply.  When done, export your mesh as STL and you're done.  Simple, no complications.

FWIW, NetFabb is intended to clean up the mesh to get it ready for printing.  Whatever edits you do afterward, will most likely break the fixes NetFabb applied, so use NetFabb only as the last step before printing the object.

I thought that was what netfabb does?

No, not automatically.  You would have to do that manually.

Additionally, NetFabb basic doesn't have any triangle reduction algorithms, so if you remove a traingle, you're left with a hole.  NetFabb can fill holes manually, but it does so in a "direct" manner.  BY this I mean it will fill a hole with as close to a straight surface as it can.  Any surface details that were there before, will be gone.

For what the OP wants to do, the best software is MeshLab.  MeshLab has simplification algorithms that will removed unnecessary triangles from a surface, but preserve the surface topology.  It can effectively reduce the number of triangles by as much as 80% without any visible fidelity loss.