Facial recognition produces potential matches. It's still up to humans to look at footage themselves and use their judgment as to whether it's actually the same person or not, as well as to judge whether other elements fit the suspect or not.
The problem here is 100% on the cop(s) who made that call for themselves, or intentionally ignored obvious differences. (Of course, without us seeing the actual images in question, it's hard to judge.)
There are plenty of dangers with facial recognition (like using it at scale, or to track people without accountability), but this one doesn't seem to be it.
The justification for depriving someone of their liberty lies solely with the arresting officer. They can base that on whatever they want, as long as they can later justify it to a court.
For example, you might have a trusted informant who could tell you who committed a local burglary, just this on its own could be legitimate grounds to make an arrest. The same informant might walk into a police station and tell the same information to someone else, for that officer, it might not be sufficient to justify an arrest.