There is some truth in this. It is the almost-exact flip side of this: If a businessman does something right, he reaps the gains. If a bureaucrat does something right, you reap the gains.
... which doesn't sound so bad, now does it?
Neither is exactly correct. If the senior management of a large company make a big mistake, they aren't the only ones who lose: some employees may lose their jobs, the company may be less effective in providing customers with useful products or services, etc. And, conversely, if they do something very right, their employees may get bonuses or pay rises and their customers may get useful things to buy. And even government bureaucrats are likely to do better for themselves when they make good decisions than when they make bad ones.
But it's a reasonable approximation. On the whole and on average, businessmen are in business to benefit themselves, and fortunately it turns out that when you have lots of people doing that it brings benefits to everyone. On the whole and on average, government bureaucrats are in their jobs to benefit The People.
And, surprise surprise, if you focus only on the downside then you see businessmen hurting themselves and bureaucrats hurting The People. But it cuts both ways.