TFA doesn't even claim that. TFA links to an advocacy website trying to convince authorities to put out less light pollution. It claims improved lighting (presumably brighter) doesn't reduce crime, and it claims a reduction (but not elimination) of lighting doesn't increase crime.
I would say that going from no lighting at all, to some lighting, on urban paths, improves safety (not tripping over unexpected obstacles) and reduces crime (presuming there was any crime while it was unlit). The article doesn't refute that. I would suggest that if a major city decided to eliminate all street lighting, it would be absolute chaos.
Nobody is trying to remove all street lighting. There are plenty of practical suggestions on here and in that document about how things can be improved without reducing safety.
From the comment that started this deviation:
> Wouldn't it be more reasonable to just expect people who want to walk places in the dead of night to wear a headlamp?