The guy who posted that did it on Sotonians and says he got his info from from someone who works for Saints so of course there's going to be a pro-Saints spin to what he says. He also claims to be recounting a conversation that took place "a few days" ago. Perfectly possible he's mixed up a detail or two.
The basic narrative we all pretty much agree on though. Negotiations between Saints and Koeman were going well, Everton offered Koeman big money (both in his pay packet and to spend), Koeman likely went back to Saints but they weren't prepared to up their offer, Koeman is likely to end up at Everton.
What you believe beyond that is largely irrelevant and mainly about spin, PR and which club you support.