As I recall (it's been decades since I did anything structural) basically a structure will fall over if the vertical projection of the centre of mass moves outside the footprint of the base. Therefore the higher up the centre of gravity is, the fewer degrees you have to tilt the structure before it'll fall over, and the wider the base, the more degrees you have to tilt it.
I think that splayed legs help because as the structure tilts the centre of gravity rises, so you have to put more energy in to achieve the same tilt, but I'm not 100% on that.
Short answer - yes.
In hindsight, the width (20") of the bench would have been perfect as the depth. Pushing on the bandsaw in that direction doesn't cause a tilt. So just an extra 4" might have been good, but then the top would be bigger and heavier then so who knows! The decision to add weight by putting it into the top definitely hasn't helped the situation.
It's a shame there's no centre of gravity overlay in SketchUp. I suppose that'd mean having to supply the mass of each component, though. I'm not really up for learning any of the Autodesk products or breaking out a load of calculations. Maybe a small scale model would've been the best.