I don't know that there ever was an exact statistical argument that led to the requirement in the USA for repeat rides to be within 0.08%.
However, this value of 0.08% appears to me to be sensibly related to the aim that courses should not be short and the 0.1% SCPF included to prevent that.
Under good conditions with little calibration constant change due to temperature, good riders can get repeatability at the +/-0.02% level. However, with a difference of 0.08% or more one could use the shortest result and lengthen the course to ensure it was not short, but then there is a risk that the course could be excessively long.
I view the 0.08% rule or (as we apply it in the UK -- guideline) as a signal that a third ride may be needed to work out what is going on.