Because following up a story is different from initially reporting it. It’s not instant, not everyone will have the contacts, many people who spoke to The Obs will not want to talk to anyone else now (reasonably so).
I suspect also that there is a hesitancy to go in heavy handed over inconsistencies in diagnosis dates etc because as a line, “man with debilitating condition isn’t as sick as maybe you thought but definitely still is sick” is not exactly the gotcha you might think. Many people might feel very sorry for him and view speculation over the exact nature of his condition to be extremely distasteful. The publisher too probably has/ feels a duty of care too. Both towards Moth (who is not after all the author) and towards whatshername. You can rightly say yes, she lied, yes, she’s been found out etc. that doesn’t change the duty of care towards her if she is now suffering a mental health crisis, say.
again, I reiterate I am not defending her. I’m just saying if, say, she’s told the publishers she feels suicidal - what would you have them do? The press is damned if it does, damned it it doesn’t.