This is merely my impression, but some who have trouble believing in coerced statements in this case seem to imagine police interrogations as conversations. They really aren't, particularly not once LE decides someone is a suspect (even an unofficial one).
I was reminded of this last night while watching a recent show on Jon-Benet Ramsey that showed clips of the interrogation of her parents. (Otherwise, the case has nothing to do with the events in Perugia.) By the time they sat down with LE, the Ramseys had been well coached by their high-powered and expensive legal team, and neither caved to pressure from their interrogators. But listening to the questioning (as in any case where tapes are available) should remind one of the multiple tactics used by interrogators.
People under interrogation are not only treated rudely and confrontationally in ways most haven't been treated since elementary school, they are faced with a variety of tactics including promises they will be released "if you can just clear up one more thing" and being told their memory can't be correct because of irrefutable "scientific" evidence. (None of this worked on the Ramseys, but as I said, they were well-coached and months had passed since the murder.)
Any inconsistency, even accidental, is treated as major evidence of deception, if not guilt. This must have been very difficult for someone as "flaky" as we've all noted AK to be, for someone as erratic with her use of language even in everyday writings.
Some have suggested that AK was treated with kid gloves until the night she was confronted with her text message to PL. But a change in attitude from interrogators may have been precisely what prompted her to make a false statement in just a couple of hours.