I think we have to make the distinction between not believing she has mental health problems and not believing the story she tells about getting help.
I do believe that she had mental problems as in difficulty adjusting to a new country, culture and hierarchy, in addition to being pregnant and getting bad press. I do not believe her story about not being able to get help.
But as for not believing she has mental problems: Most people will think 'people do not lie about mental health problems'. No one wants to not believe people who say they have endured something terrible, but we do know it happens.
Research (2017, De Zutter) gives 8 reasons why people make a false accusations of rape. Some of below are also relevant to lie about other serious things, like mental health:
- Material gain: to receive money, professional promotion or other material benefits.
- Producing an alibi: a false allegation is used to cover up other behaviour, such as being late or absent to an appointment.
- Revenge: to retaliate against a disliked person by damaging the reputation, freedom or finances.
- Attention: an attempt to receive any kind of attention, positive or negative, by anyone.
- Sympathy: a special kind of attention-seeking whereby the complainant tries to improve a personal relationship with a specific individual.
- 'A disturbed mental state'; this may include false memories ("sexual hallucinations") or pathologic lying.
- Relabeling: consensual sex is relabeled 'rape' to the police, because of its 'disappointing or shameful character'. De Zutter et al. argue that a distinction should be made between some acts during a consensual sexual encounter that a participant did not want or had no desire to engage in but nonetheless gave consent to (e.g., to please their partner) on the one hand, and rape (nonconsensual sex) on the other, but that many lay people and even some scholars do not make this distinction and confuse the two. It is often when accounts of such 'unwanted consensual sex' are told to friends and family that the latter interpret it as rape, and put the complainant under pressure to file an allegation.
- Regret: after having had consensual sex, a complainant experiences negative feelings such as disgust, shame, and sorrow; when others notice this and ask about the source of these negative feelings, they are prone to view the encounter as rape and put the complainant under pressure to file an allegation.
(This is the order from Wiki, I didn't change it)