Looking at the video link:
The example of the two cylinder-shape mesh where you want to reset the bounding box, is definitely not a "bug". If you look closely you will see the Reference Coordinate System is set to View. That is why the Transfror Gizmo does not align with the bounding box. If it was on Local, the Transfrom Gizmo would be aligned with the bounding box and the Mirror command would work as expected.
Not a bug at all. It is working as designed. The problem is due to the way the original mesh object was created. However the solution used to re-aliging the Pivot Point is well known. Works on other things such as trying to Extrude an imported Spline only to have the extrusion go sideways (Local Z-axis not aligned in the desired direction).
He does have some modeling tips that are worth looking at.
A true "bug" is when a command or feature does not perform as expected, not necessarily as a user expects, but not expected as designed. Symptoms of a bug might be a quick exit to the desktop, or trying to refine a spline and the vertex jumps to the end of the segment.