I feel it could come down to not using statistics to infer a given conclusion.
For instance base probability accounted, if there was a 1 in a trillion chance someone was at the right place the right time, just straight assuming it couldn't happen by chance is still wrong. By definition that chance was not 0.
At some point a practical decision could be made to cut prosecution cost, but it should be understood that nothing was proven.
I think the legal system understands quite well that it doesn't prove anything (in the mathematical sense), which is why it has different standards of proof.
A 1 in 1 trillion chance would be considered both "beyond reasonable doubt" (enough for criminal matters) and satisfy the much weaker "balance of probabilities" usually applied to civil matters.
Of course there are plenty of examples to point to where people were convicted despite very reasonable doubt.
And if that even happens a lot in the world (e.g., many nurses looking at many patients every day), then that chance is quite likely to realize somewhere.
For instance base probability accounted, if there was a 1 in a trillion chance someone was at the right place the right time, just straight assuming it couldn't happen by chance is still wrong. By definition that chance was not 0.
At some point a practical decision could be made to cut prosecution cost, but it should be understood that nothing was proven.