“They could simply name their source(s) if they wanted to be taken as credible.”

Not if they want sources again in the future. Assuming they have credible sources, it will prove them correct in due course. The vast majority of people aren’t grading news outlets on a minute-by-minute basis like this: if they read in People first it was his son, and two weeks from now it’s his son, they’re going to credit People with being correct and where they learned it first.

And if People burned the sources who told them this, industry people would remember that, too.