ok465:
The sidestep minimums are only associated with the ILSs, not the runways.
The RNAVs have no sidestep minima below basic VFR, not even circling.
LAX was the "test case" for side-step minimums. They came about when all CTL minimums for the airport were deleted. RNAV wasn't even a dream at the time.
Besides, no one flies RNAV approaches at LAX. Having said that, RNAV side-step minimums are authorized in FAAO 8260.19F.