Ok. I think I'll venture a guess. It was Mr. Green in the Parlor with the rope... no, just kidding.
Seriously though, here's my thinking.
I would speculate that a raccoon found a clutch the prior night, within the complex of buildings, and decided to take the food elsewhere to eat (or a mother taking food to offspring, perhaps). It is a known behavior of raccoons, which sometimes includes finding water to wash their meal. As he or she, moved from the clutch they came across Rex's part of the shed. The dog's reaction startled the egg bearing critter, who unintentionally dropped an egg on to Rex's bed, perhaps from the top of the wall and in the haste to get away, leaving it undamaged because the bed was relatively soft. It is even possible that the raccoon was walking across the dog's bed when one or more dogs awoke, but I doubt it. Running in fear for his or her life, the raccoon continues up the walkway but manages to drop another egg on the brick, this time damaging it on the harder surface. This likely happened when the raccoon needed to go from the steps and begin his or her ascent up the side of the house, by the door to get to higher ground and likely the location of the raccoon's nest.
Is that close?
BTW, I wondered why everyone thought that it was Green in particular and not his parents? I am curious about another thing too. Who put the flowers next to Green's grave?