No, we're not talking about that. The stories lifted by the Sun all appear on NewsNow which, while hardly on the same level of an agency like Reuters, do have strict editorial guidelines by which sites must operate otherwise they are de-platformed (funnily enough, the Sun's content doesn't meet NewsNow guidelines).
Once anyone (and that goes from fan-led content like H&H, to tabloids, The Athletic or even Reuters/PA) start talking about 'sources' giving them a line, it becomes almost impossible to disprove - as well as having some protection. Until you can prove it is true or bollocks, you take it at face value. It's something I'll often do - particularly with Football Insider 'exclusives'. We'll report what they have claimed (often adding in opinion on whether it seems plausible or not) and try follow-up as soon as possible with information from my own 'sources'.
While, I have my own personal experience with Football Insider which sours me on them, Wayne Veysey (their editor and the named writer on the Gerrard/Leeds story) is a relatively-reputable journalist down south.
The second point, you seem to miss. There's a fine balance to be struck. Absolutely, robust and accurate reporting is key but there are also commercial demands to be met for papers like the Sun. They need to get clicks to generate revenue or everything goes behind a paywall.