I don’t think it’s evil that people are speculating, just human nature.
A horrible and unknown thing has happened to a woman, her children are sat at home scared and hopeful that their mother will come back while many know it’s increasingly unlikely.
It makes people feel fear, anger and impotency. They feel moved to ‘help’. But what can the vast majority of us actually do to help? Absolutely nothing.
So people talk, and puzzle over it. They might look at (an out of date) Google maps and spot that the river is littered with fallen down trees. Or that the caravan site is very close to where she went missing. And talk about other possibilities, because none of us like to think that we could just be gone that quickly because of an accident (we could).
And because people aren’t personally involved with her it does become a bit like one of those programs where you try to ‘solve the mystery’.
You will never stop people speculating and talking about a tragedy with some mystery thrown in.
As long as people aren’t actively attempting to contact the family, or going to the site and disrupting the police investigation, I don’t think what is happening is anything that can be stopped or reasoned with. Just human nature.