Does a fat tire ride softer than a skinny one at the same pressure? Fat tires are associated with good bump absorption. Is this due to their fatness, or is it due to the low pressure with which they can be used?

If I pump a fatbike tire to 120 psi (yes, that would be absurd), will it still absorb bumps better than a 23mm tire at the same pressure?
After reading the answers here and becoming more curious, I found this article, which agrees with @Daniel.

to briefly summarize it, they found that at the same tire pressure the narrower tires deflected more and had a lower stiffness (force over displacement)



A curious finding is that a difference of 1 bar (14psi) makes more of a difference that a 5mm tire change. I suppose the problem becomes that with a 23mm tire there is only so much room for compliance. Additionally, they found that tire width had very little effect on small bumps (8mm in this test) and that the main factor was tire pressure:


  at this point it seems that for bumps smaller than the tire diameter, the shape and size of the bump is driving the stiffness more than the effective width of the tire itself.


That article also links to another article which discusses the sensation of tire stiffness as an expression of hoop stress, which they call casing tension. To me, this seems like a much more logical explanation as to why a wider tire will feel stiffer at a given pressure (again agreeing with @Daniel). I would suggest reading the article, but I did my best to briefly explain the end result. Essentially, the equation for hoop stress is based upon wall thickness, diameter, and pressure. 




  Wall thickness = the thickness of the tire casing
  
  Mean diameter = the tire size
  [cross sectional area of tire]
  
  Pressure = the pressure the wheel is inflated to


Maintaining a constant casing tension and wall thickness we can solve for pressure and see that the pressure is inversely proportional to the diameter.