Grasses in the Miocene..._Bullockornis_ in the Miocene.
Well... or Oligocene.
Re: "ordinary tropical rainforest". This quote is from _Magnifiscent Mihirungs_, by PF Murray and P Vickers-Rich, (2004) talking about popular paleontological misconceptions: The vast majority of Australia's vertebrate fauna evolved in, and were adaptive responses to, scleromorphic woodlands that grew in any precipitation regime...it is about time we retired this old rainforest flag." (don't have page number--quate is under fig. 215).
Then what is Riversleigh???
Several factors relate to why Australia. Any continental ground-nesting bird has to either hide or defend. If it hides it must have an effective concealing medium (e.g., grass for ostriches).
Why do you think a rainforest is less effective?
Murray and Vickers-Rich note that egg shells have not been found at most sites where predators are abundant.
AFAIK dromornithid eggshells are only known from *Genyornis*.
In either case, concealment may not have been primary if predator density/potency was low enough.