I was listening to Andy Goldstein and Jason Cundy on TalkSport on Tuesday evening (same day that Koeman to Everton was confirmed) and they were similarly struggling with the concept of a Premier League club having a different operating model, despite several Saints fans phoning them up to explain what you've outlined above. They were saying it proves how "little" a club Southampton are when they rollover and let clubs like Everton poach their manager, with no regard to the fact that it might have been in our interests to let him go n the circumstances.
p.s. don't ask me what I'm doing listening to TalkSport at 10pm at night. It was a momentary lapse of judgement and I promise it won't happen again