I don't see this. Koeman is a good manager with a longer CV than De Boer and one that includes some success in the prem. To say that Southampton only marginally over-performed the last two years is a bit disingenuous; I could point to Arsenal, Chelsea, Man U, Man City, Everton, Liverpool, Tottenham, West Ham, and potentially even Stoke, Swansea and Palace who, on paper, should have been better than Southhampton the last two seasons, not to mention Leicester who found a way to win the league. Southampton's marquee signings this past season were van Dijk and Charlie Austin - not exactly world beaters.
I'm just not sure who you expect us to sign. Emery I understand, but he's about the only option I see as having a higher ceiling than Koeman, and as we all well know, Spanish managers don't always transition well to the Premier League. We're not stealing Pochettino, we were never signing Mourinho, Pellegrini has less promise and is a far more known quantity. Just who is exactly is all this money supposed to get us and which bigger club (because there are bigger clubs than us) are we stealing him from?