|MadSci Network: Genetics|
The short answer to your question is that "Fingerprints and physical appearance in general are part of an individualís phenotype, which arises from the interaction of the individualís genes and the developmental environment in the uterus."
This is explained further in the following article, entitled "Phenotype v. Genotype: Why Identical Twins Have Different Fingerprints".† The 1st 2 answers to the question, "Why don't identical twins have identical fingerprints?", from the NewScientist, and the answer to the question "Do identical twins have identical fingerprints?" are also instructive.
So your conclusion is essentially correct, in that there are environmental, as well as genetic, influences on fingerprint development, contrary to what one might intuitively expect.† Apparently it's primarily dependent upon small differences in the intrauterine environment, as "Fingerprints form before birth and their shape is generally believed to be influenced by nutrition and the growth of fingers during the 13th week of pregnancy", according to the ScienceNet.
Thanks very much for the excellent question & the opportunity to contribute to the MadSci Network fingerprint development database!
Try the links in the MadSci Library for more information on Genetics.