What does ‘One’ in “Detectives slapped handcuffs on her. “You know you did it,” she said one later shouted at her. “Just admit it.” mean?

Solution 1:

It stands for one of the detectives. This sentence is poorly constructed, because it is difficult to parse; but it is syntactically correct. The conjunction that has been omitted (which is fine in itself).

“One night, Ms. Sumasar was pulled over by the police. Before she could speak, detectives slapped handcuffs on her. “You know you did it,” she said that one detective later shouted at her. “Just admit it.”

In a simpler sentence, this construction would be fine, because then there'd be no cause for confusion:

The picture she said I had stolen was in her attic.