You could place guide points or guidelines inside the component, using the Tape Measure tool, or a plugin such as Matt66’s PointTool from the SketchUcation plugin store, by inferencing from relevant extremities of the model.
Use the keyboard arrow keys to constrain the inference along Blue axis (up arrow), Red (right arrow) or Green (left arrow) as appropriate, starting from an extremity.
Not sure if this solves your problem, but it’s what I make of the situation. I have a few options.
1* This is the simplest, Its been mentioned already. The axis is in an odd place, so the component (top level) is exploded then made back into a component, making the axis return to a normal place.
The component is deleted (but remains in model) then dragged back in from the in model components window, you have the new origin as you drag it. Simply place it onto any point of your choice.
2* This will second option will move the axis from an “odd place” to an intersection formed by guides, this is roughly the normal axis placement.
Again, the component is deleted (but remains in model) then dragged back in from the in model components window, you have the new origin as you drag it. Simply place it onto any point of your choice.
No. There will always be endpoints that are in the planes of the sides of the bounding box, at least 12 endpoints determining the bounding box, at least one endpoint per side. That is how SketchUp creates its bounding box. The outermost endpoints of the shape or selection (whatever that may be) according to the current drawing axes. So in your case the sphere of the chair has (hidden) endpoints that may help you to reposition the axes to the corner of the bounding box.
But with a chair I would ounly wont the leg(s) to sit exactly on the ground. The rest is eyeballing, just as @DaveR’s posted above.