Well, they can start by interviewing them individually (and in person) and making sure that Jill has her daughter with her when they interview her. Is it possible this is all true? Sure. But in my experience, I think it's more likely it isn't.
Forget the fiance, Jill just left her son and ran off? Ok, we could say some moms may do that. But it goes against everything her family said and believes about her. It's out of character for her, it seems. And then why has there been no trace of them? No cards being used? Nothing. They knew they were being looked for; of course they did. They didn't want to be found? Ok, fine. But why not call your son at the very least or your parents so they don't think you're lying at the bottom of a lake somewhere or you're being tortured and raped for the rest of your days? They're adults. They didn't have to do this in hiding. They could have run away together and started a new life in privacy without all the cloak and dagger stuff.
Like I said, is it possible she went willingly and intentionally hasn't gotten in touch? Intentionally hasn't used her credit cards? Intentionally allowed the police to search for her, drained resources that could have been used for other things, and allowed her family to be worried sick? Yes. But it's way more likely that he is pulling the strings in my opinion.