She could have been the subject of public sympathy here.
If your estranged father becomes embroiled in serious allegations, many people will instinctively feel sympathy for you. You didn't choose your parents, and you're not responsible for their behaviour. A brief statement expressing concern, respecting the investigation and maintaining her distance would have allowed that sympathy to remain focused on her circumstances. She should have stopped after the first paragraph.
But once you start explaining, commenting or making statements that people perceive as contradictory, the conversation changes. Instead of discussing the allegations, people start discussing you. What did you know? When did you know it? Why are you speaking now? And how does this fit with what you said previously?
And I think the biggest mistake is failing to recognise that you don't have to defend yourself against a criticism nobody has actually made yet. By trying to get ahead of the narrative, you can inadvertently introduce questions that might never have gained traction otherwise.
They see criticism as something that must be corrected, rather than accepting that public opinion will never be entirely within their control. They risk responding to the immediate controversy rather than considering the long term consequences. What feels satisfying to say today might be difficult to defend tomorrow. They also underestimate how much their previous public statements shape the interpretation of their current ones. Once people perceive a pattern, every new statement is judged through that lens.
Of course, we can't know their private thinking or whether every public response is their own decision. But the communications problem is clear. When people already scrutinise your every move, you have far less room for error.
And here's the irony: the royal family's approach of saying very little can seem frustrating and evasive, but it also prevents them from creating an endless supply of new material for public debate.