There are definitely false confessions. They are not as common as the false “eyewitness identification.” (Most of the DNA exonerations have been on cases where there was a false identification.) But they do exist. The police tend to get a theory of “what happened” into their head fairly quickly on an investigation, and once they decide a crime was committed by a particular person, they zero in on them to the exclusion of all other possible alternatives. And the police are trained that they have to break down the psychological barriers of denial in a suspect. It works very well to get guilty people to confess, but when faced with the same techniques, sometimes they work on innocent people too.
A fair number of the DNA alleged exonerations involve confessions.
I’m predicting a scandal in a few years over these false negatives. Attorneys are already in a position to challenge positive DNA results as unreliable in paternity cases. If the positives can be unreliable, so can the negatives.