Media organizations get pretty good at distinguishing between rumor and leak. Any major one will have all sorts of policies on how a story gets verified, and they tend to work. Mistakes do get made, as with anything involving humans.

> What reason do we have to believe these four people?

The media organization involved deems them credible enough to use as sources. It's left mostly up to you whether you trust that media organization.

> I guess it is the reputation of the journalist on the line if the rumors turn out to be false.

Yes, essentially (and their editors, and the publication, and the media as a whole...). This is why reporters cultivate sources, vet their information, keep track over time of their reliability, and generally require multiple independent sources if those sources are leaking anonymously.