I'm a forensic pathologist, and my lab does DNA fingerprinting.

DNA fingerprinting and associated techniques are reasonably associated
with any and all of the following fields:

Biochemistry
Molecular Genetics
Clinical Pathology
Forensic Pathology

At the Armed Forces Institute of Pathology, where I work, we have
three labs which are competent in the techniques; these are the
Biophysics Division of the Department of Cellular Pathology,
the Molecular Pathology Division of Cellular Pathology, and
the Armed Forces DNA Identification Laboratory of the Office of the
Armed Forces Medical Examiner.


The methods are right smack dab in the middle of the area of competence
of the molecular pathologist or  molecular geneticist.  It is slightly
off the center for general biochemistry, but a good biochemist could
quickly come up to speed, and likely has some training in the area.
It is a little marginal to the classical population geneticist, and
he or she would likely need extra training.

The methods are part of the day-to-day hands-on practice
of Forensic Pathology. In general, however, a forensic pathologist hands 
the sample to the lab guys.  Still, the forensic pathologist has to know 
the basics in order to know what to get, what to order, how
to interpret results, etc.  He or she will had introductory training 
in the area, and could come up to speed relatively quickly, but
doesn't touch the machines on a day to day basis.  It's like dealing
with poisons -- I know a lot about poisons, but I haven't touched
a gas chromatograph/mass spec in 10 years; we have toxicologists
who do that stuff.  If I had to, however, I could get through it
if I had the manuals and such.   

Laboratory medicine is a part of general training in Pathology, and 
a general pathologist would have a good grasp of the general area, but 
would need a bit more work to come up to speed.  A person in general 
clinical medicine such as an internist or surgeon would be at a loss 
unless he or she had extra training in the area. 

Modern PCR analysis for DNA fingerprinting is getting easier and 
easier, which the introduction of packaged tests, etc.  There
is less need for the technical skills of making gels, packing
columns, etc. and it is becoming more and more an automated test
which can be performed by  those with less competence in 
experimental methods.  At higher tech levels, doing DNA analysis for 
standard markers will be about as difficult as doing in-home 
pregnancy tests.  Thus, you sort of need to distinguish between
"standard" DNA analysis skills and "experimental" skills.  
One doesn't have to be a specialist any more to test for 
sugar in the blood or urine, pregnancy hormones, etc.  Similarly,
testing for DNA markers will require less and less specialized
technical skill.  On the other hand, designing new tests, or
testing for unusual features will still be the strength of
the specialist.