Background: I do not work for Amazon and I have no knowledge of the internal workings of their specific system
I've worked in the biometrics industry for quite some time. The headline and implications sound all very scintillating unless you know how real systems work and are used.
With most algorithms, when you match two faces you get a "score". This score basically means "likelihood of the two faces being a match". When you run these through a system, you typically set a score threshold. Let's say the match confidence score is on a 1-100 scale - 1 being very unlikely to be a match, 100 being highly likely to be a match. You might configure the system to say "Give me all results where the score is 75 or above". Now, you are probably going to look similar to a fair number of people in the rest of the population, at least according to the algorithms. So they don't take the person with the highest score and put him or her in prison immediately. There are human operators and law-enforcement agents that would take the matches with the highest scores and 1) Visually inspect them to see if they really are that close or not 2) Do a quick background check to see if this person has been charged with related crimes previously 2) at the next level, do some research to see if the person that is a match could even be reasonably said to be in the area of a suspected crime at the time it occurred. Only then would the matched person even be brought in for questioning, much less charged with anything.
So the fact that some subset of politicians have a 25% match rate using some threshold score value in a database of gosh-knows how many known criminals is not that far-fetched, and does not indicate that a suspect that might match the database at the same rate would be cuffed and brought immediately to prison.
Now I'm not a fan of scanning entire crowds of people at an event or populated area hoping that you catch someone with an outstanding warrant, etc, which is a different issue. But the headlines and implications thereof grossly overestimate the role of a raw match in the larger process of investigating a crime.