What you call "petty bribery" are vast networks where people at every level squeeze citizens for bribes, take their cut, and pass the rest upwards to their superiors. People who run the country are the bosses of various bribery chains whose influence depends on the depth and width of the corruption network. They are like competing mafia families: military mafia gets money by skimming contracts and squeezing people for bribes to get their children out of forced conscription; legal mafia gets money by selling verdicts; etc.

It's funny that you mention corporate lobbying. In a truly corrupt place, companies are treated no better than citizens. Companies are squeezed for bribes too, and if they resist, then companies get raided and taken over. Owners get imprisoned on made up charges (or, ironically, for past bribing that they are unwilling to continue) and new owners are installed, usually members of the same corruption network, such as children of officials. In places like Russia, the equivalents of governors and congressmen are all owners of factories, oil terminals, ports, banks and other major businesses. They just steal the companies. It is impossible to run a successful major company without being one way or another a piggy bank for the corruption networks, permanently at risk of losing it all in illegal takeovers. (I recommend Bill Browder's books if you'd like to know more.)

The western world has so little corruption that an average citizen or company never experiences anything like this.