IIRC, part of the problem is that fingerprint comparison methods do not produce consistent results. Different experts produce different results with the same set of fingerprints.
Also, as the article says, fingerprints 'in the wild' are often incomplete, smudged, etc.
EDIT: From the National Academy of Sciences report linked to from the article (the ACE-V method is the standard fingerprint analysis):
the ACE-V method does not specify particular measurements or a standard test protocol, and examiners must make subjective assessments throughout. In the United States, the threshold for making a source identification is deliberately kept subjective, so that the examiner can take into account both the quantity and quality of comparable details. As a result, the outcome of a friction ridge analysis is not necessarily repeatable from examiner to examiner. In fact, recent research by Dror23 has shown that experienced examiners do not necessarily agree with even their own past conclusions when the examination is presented in a different context some time later.
> If the suspect is a better match than N(1-p) of the other fingerprints, then the match has a p-value of p.
There may be no way to objectively determine if the suspect's prints are a better match than others.
More generally, I lack your expertise but it seems to me that statistics require data; we may not have reliable data. More colloquially, garbage in, garbage out.
Anyway, I recommend the National Academy of Sciences report, which is authored in part by their Committee on Applied and Theoretical Statistics.
Also, as the article says, fingerprints 'in the wild' are often incomplete, smudged, etc.
EDIT: From the National Academy of Sciences report linked to from the article (the ACE-V method is the standard fingerprint analysis):
the ACE-V method does not specify particular measurements or a standard test protocol, and examiners must make subjective assessments throughout. In the United States, the threshold for making a source identification is deliberately kept subjective, so that the examiner can take into account both the quantity and quality of comparable details. As a result, the outcome of a friction ridge analysis is not necessarily repeatable from examiner to examiner. In fact, recent research by Dror23 has shown that experienced examiners do not necessarily agree with even their own past conclusions when the examination is presented in a different context some time later.
Don't miss that last sentence.