I don't doubt that they were indeed well compensated, however they might still have ambitions or want to be payed more. that is the business side of things, I'm sure Southampton fans are sick if and mad because it keeps happening and probably demanding Liverpool head for it.
I'm pretty sure Southampton fans are happy to be where they after 8 years out of the top flight but obviously all fans want to keep their best players. But that's besides the point, you made out like there was some sting by the Southampton board involving private investigators because they're upset about getting lots of money for their players, in some instances, more than they they're worth (Lovren, Lallana, Lambert). That's not the case here. They would sell at a record price for a defender, there's no doubt about that, but LFC trod on some toes by leaking to the press and that's what has pissed them off. All transfers involve tapping up to some degree and all clubs do it.