This is not simply because they come from the same social class. Nor is it because MPs are bought off by the rich. It’s also because of a selection effect.
The sort of people who want to enter politics - as MPs, advisors or even reporters - are generally those who think that society and the state can be managed for the better. They are, therefore, predisposed to believe that management is, or can be, a socially useful activity, which means they are biased to think that chief executives, on average, should earn a lot.
The counterpart to this bias is that they underweight reasons to be sceptical about management. They overlook the possibility that limited knowledge, cognitive biases (big pdf) and diseconomies of scale undermine the general effectiveness of management. Even more worryingly, these biases causes them to downplay the extent to which managers are rent-seekers who use their power not to improve organizational performance but to extract cash for themselves.
Worse still, politicians don’t realize they have this bias. Because they are surrounded by like-minded people, they don’t see that their perspective is a biased and partial one; they are afflicted by deformation professionnelle. And the media, far from correcting this bias actually reinforce it - partly because they themselves have biases towards hierarchy, and partly because their pretence that “balance” consists in merely giving equal weight to Tory and Labour MPs squeezes out alternative views.
The upshot of all this is that we have a political-media class which is excessively sympathetic to bosses - and unreflectively so. In this sense, the state helps to protect the interests of the rich not (merely) because it has been bought, but because of selection and ideological mechanisms.