Demonstrably how?
> Why would you assume that we would act righteously in the absence of law?
What is a demonstrably false fairy tale is that we don't act righteously when law enforcement is present. So asking what would happen in its absence seems irrelevant.
> It is painfully obvious that we would act much worse under anarchy.
Above you said it was "demonstrable" but now seem to be settling for saying it's somehow self-evident.
...
Fwiw I don't personally agree with the quoted statement, or rather I agree with only a narrow interpretation of it.
I don't think individuals are capable of behaving in a reasonable fashion in all situations without having to be forced to. I do think groups are capable of behaving in a reasonable fashion without external force, given certain conditions: anarchism in my mind is about local* law enforcement rather than external.
Self-regulating organisations are possible, the only real condition is the removal of external incentives for those organisations to misbehave.
*By "local" I just mean internal/within proximity to the individual