It sounds like they used fingerprints correctly.
Wrong way to use fingerprints: "We have a crime and no suspects, but we have a fingerprint. We ran that through our database, and got a single match. That must be the person who left the print".
Right way to use fingerprints: "We have a crime and several suspects that we know were deeply involved in the matter that the crime was part of, but we don't know which were actually there during the crime. We also have this fingerprint left during the crime, and it matches exactly one of the suspects, which shows beyond a reasonably doubt he was there".
It's really no different from hair color, skin color, sex, height, weight, age, or DNA--the evidentiary value of a match on any of those depends on how that thing is distributed in the population that you can show by other means includes the correct person. The more you can narrow down that population, the better the evidentiary value.
Take sex for an extreme example. A woman reports that a man assaulted her in New York. There are a lot of men in New York, so if that's all you have to go on it is pretty worthless. But suppose an officer saw the attack, got a good enough look to see that the attacker is a man but nothing else, and saw that man run into a women's restroom to hide. The officer enters the restroom, and finds that it is occupied by two women and a man, and there is no way out of the restroom except the door the man entered by, which the officer had under observation continuously from the time the man entered to the time the officer entered and saw the three occupants.
Convicting that man for assault would be quite reasonable on the above evidence, even though it is largely based on the fact that he is male and the assailant was male. That's because other good evidence narrowed the population of possible assailants down to just three, and so if you can conclude that the assailant must be in that group, then the assailant being male does show that he was the assailant.