that is more likely than all other ideas. I haven't seen an operculum but should collect some and check again. Some have little holes; if these balls were insect eggs, the holes might indicate parasitism.
hi DonFletcher Puzzle solved I collected and took photos today: Fruits of Exocarpos cupressiformis ; see sighting Exocarpos cupressiformis (Cherry Ballart) and https://spapps.environment.sa.gov.au/SeedsOfSA/speciesinformation.html?rid=1928
abread111 birds eat the red succulent pedicel (the "cherry") with the hard fruit (nut?) and release the undigested hard fruits with their droppings. The fruits are very light and presumably transported by water; they accumulate where conditions are suitable - as shown in the South Australia link that I included in my comment above. I found several patches with large amounts of fruits under or close to Cherry Ballart trees.
The similar photo in the related species shown in the SeedsOfSA website is of an emu scat. Maybe foxes eat the "cherries" here like they do briar hips and this is patch of "peppercorns" is a fox scat.
foxes are good climbers but I don't think they are climbing up the trees - birds seem to to be more likely. Actually the rare Little Friarbird was observed feeding on Cherry Ballart "cherries" in the area, see this records of a Little Friarbird sitting in front of a Cherry Ballart: Philemon citreogularis (Little Friarbird) and Philemon citreogularis (Little Friarbird); the photos were taken close by. I expect also Currawongs they are attracted to red (such as my tomatoes) and numbers around The Fair have vastly increased.