In fact, Mr. Mayfield wouldn't even have suffered so if computers couldn't already do this job: it's quite unlikely that the FBI has enough staff to compare twenty-year-old military service records to Spanish bombing evidence by hand. The problem, as you nearly realized, was the threshold used in the query. There were no actual matches, yet the FBI required twenty "matches" to "investigate", so it produced twenty "matches". If the FBI had been a bit more overstaffed/bored, they would have pulled 100 "matches". It's like when we pull receivables out of the billing system to write off at the end of the fiscal year: the CFO tells us what the final number should be, and we just get the oldest accounts that sum to the proper total.
You seem to have missed the point, though, which is that if fingerprinting must be done with detailed knowledge of the field agents' pet theories, that implies fingerprinting is not scientific.
Taking a print is not perfect, even in perfect conditions. From a print in an object, not good at all.
And a lot of people have similar prints. You can't have one print you recovered from some place and find a perfect match with 100% confidence in a database (your target may not even be on the database)
Having a known identity and matching a provided sample to that DB is much better, as is having a smaller DB (for example, entering a gym)
So, yes, you can have a computer finding candidates but then you can have a human to match it more carefully (that's what the Spanish did apparently)
I'm also not sure your assertion that being scientific makes it easy to encode in software is true (easy of course being a relative term).