Thanks, that source doesn't have anything quite resembling the quote in question though.
Another english source had -
Police detained all three after Knox allegedly broke down and confessed. One officer said: "The story kept changing and didn't square. In the end she just collapsed. What she told us helped bring the case to a close but it was only a matter of time.
Heh, that one implies they didn't even need Amanda's statement to 'close' the case on Patrick!
Here it is from Barbie Nadeau:
"Initially the American gave a version of events we knew was not correct," Perugia police chief Arturo de Felice told reporters. "She buckled and made an admission of facts we knew were correct and from that we were able to bring them all in. They all participated but had different roles."
Arturo also indicated what the 'facts' were,
from a Telegraph article:
"The police chief, Arturo De Felice, said Knox had "crumbled and confessed" under intense questioning. "There were holes in her alibi and her mobile phone records were crucial," he said. Police also found text messages from Lumumba, fixing a meeting between them at 8.35pm on November 1, the night Miss Kercher died."
Patrick and Amanda exchanging texts was the primary 'evidence' they brought before Matteini, along with with the statements Raffaele and Amanda signed and a 'witness' to Patrick's bar being closed, that Patrick couldn't provide an alibi and that his cellphone records indicated he was in the vicinity of the cottage that night. They ginned up a report suggesting a vague match between Rudy's shoeprints and Raffaele's (they both wore Nike but different models) to suggest an exact match. They knew from the DNA work being done that there was a 'unknown' person (Rudy Guede) who'd left their DNA all over the murder room, and certainly had the ability to figure out from the haplogroup it was likely to be someone of African origin.
It must have seemed so 'obvious' to them, especially with Patrick calling down to the Questura the day of the discovery ('he's worried about what she'll say!") and then meeting with Amanda the day of the interrogation, as reflected in the second statement. There were also reports of them finding an 'African hair' in the murder room, but they didn't mention much about that after the hairs they collected didn't match any of the suspects and they decided to blame Patrick's arrest on Amanda, which unfortunately they've gotten away with to this day amongst some.