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As of 2004, the FBI had 46 million individual computerized fingerprint records, and around 200-300 million cards.

If we disregard duplications and generously say that there's 400 million total sets of fingerprints on record in the US, that's 6.7% of the 6 billion population of the world.

The belief that no two people have the same fingerprints is unproven, and can't practically be proven.

I'd probably be hard-pressed to convict if the ONLY piece of evidence they had was a fingerprint from a crime scene and an AFIS search that turned up an otherwise unconnected suspect.

If they had even one nice neat fingerprint then that would be very strong evidence indeed, but putting together fragments from several different fingerprints strikes me as very problematic. To my understanding (it's been a while since I've read about this) fingerprint analysis is done by mapping out the points and angles of the lines. IIRC, about 16 points of comparison are used in a full thumbprint (don't quote me on that). In any case, a big part of the reliability involves the relationship of the points and angles to one another. How do you reach a reliable ID putting together points of comparison from partial prints of different fingers? If you use only fragmentary prints then you can get a positive ID on two different people, because what makes fingerprints unique is the unique arrangement of the same universal features.