Part of the process of veing arrested and questioned includes the police saying very clearly "anything you say may be used in court". Their job, and that of the CPS and the prosecution team, is to "prove" guilt. Your defence team / legal representative knows pretty much anything can be used in that quest, by implication and insinuation at the very least, right up to stating as fact that something you said means x, y or z, bolstering your alleged guilt.
Given that there were three arrests in total, aside from all the valid perspectives from other posters about how prolonged psychological pressure affects people differently, Lucy's legal team would have been schooling her on the best approach, because they know all too well how suspects can shoot themselves in the foot quite innocently.
For example, the idea that offering an alternative explanation would be appropriate. If it was outside of her field of perceived expertise, it could be used to suggest she was arrogant, or had deliberately researched to throw suspicion off her, even if she was innocent, it could be used against her.
As for weeping, wailing, or being perceived as obstructive - all could lead to negative legal consequences, for example resisting arrest.
If you have never been accused of something awful, and are innocent, you may well have faith in the system, and that everything will be fine as long as you tell the truth. There are multiple systemic reasons why this is a naive approach, and why you depend on a good legal representative of your own.
Criminal court (and "family court") are about winning or losing. Where the "truth" is elusive or complex, it becomes the first casualty.
While people on both sides may truly believe in the guilt or innocence of a subject, they have vested interests in winning, sonetimes at all costs. An ordinary person is David in the face of Goliath, and the system, once rolling is a juggernaut that is very difficult to stop, especially in high profile, expensive and complex cases.
This case should hinge on the medical evidence, which is flawed and was proposed by an "expert" who could easily be accused of arrogance and hubris. There aren't many occasions when a judge will write to the judge of an ongoing case to express his alarm at the reliability of said witness. And it should have been taken much more seriously.