Since there is no manual for the 3D Print Toolbox yet, I had to consult the source script to find out how they check for the zero faces. The default cube was used for testing.
The script looks for faces that have an area less than the given threshold. When you use Blender with the default metric settings then 1 Blender unit is 1 meter. And the face areas are also calculated in square meters (m²). The threshold is the value of the Degenerated setting. The default value is 0.00010
and it's also measured in m².
Because 0.0001 m² is 1 cm² (=1 cm x 1 cm) the script actually checks for faces that have an area less than 1 cm². And since your model is 13 cm tall when the scale is applied, this is a pretty big value for testing and results in a lot of reported faces.
In the end, you probably just need to lower the threshold and adjust it to match the 3D printer's resolution in m².