I think it's wrong he who pays the money calls the tune, we pay the money so we call the tune, they are here to serve us, we are their bosses, that's why we get to sack them every 4 or 5 years.
You cannot serve 2 masters, you cannot wear 2 hats, you cannot be impartial when you are employed by someone else also, there is often a conflict of interest I'd wager and given that they will be privvy to sensitive information it could give some firms an unfair advantage.
Their houses are paid for by us, their furniture is paid for by us, their is subsidised by us, their canteen is subsidised by us, their travel is paid for by us, their postage is paid for by us and their partners and children are often employed by us (although I'm sure they interviewed other suitable candidates first, NOT) what more do these people want?