Usually "true capitalism" means one of two things:
1. Capitalism where there is no government or regulatory interference, and the "invisible hand of the free market" produces some kind of utopian society based purely on every business abiding by rules enforced by no one, where somehow corporations don't take advantage of workers they way they do now despite there being no laws against it.
2. The same thing but sarcastically because it's obvious that that system would be demonstrably worse than the restricted version of capitalism that we have now.
The "invisible hand of the free market" works only, if you have many market participants competing one against another. When a participant wins the competition you get monopoly, when multiple participants collude you get oligopoly, or cartel. Market can not solve this.
Where does capitalism mandate corruption? Yes, it is not realistic to assume there is no corruption, but capitalism in and by itself does not mandate corruption.
Obviously this all falls apart when capitalism can buy legislation. We are seeing how the USA is currently eroded by a few oligarchs.
They're not saying it 'mandates' it as law, but that the systematic incentives inevitably lead to corruption. The ability to buy government is irrelevant - this is just the easiest method right now of converting money into power. If there was no government to buy, private business would execute that conversion themselves by ruling over people and enforcing their wishes directly.
"capitalism" was meant to harness the greed in men- they're self-assembling groups on mostly level playing fields, and the people vote during every purchase. The more votes they get, the more opportunities to expand. Only when the people fail to choose wisely is a governmental body supposed to come in and help "regulate". The other option is the government decides from on-high how things should work, and you'd better hope that what got them to power was good. Then these people need to be wizards at allocating labor, research, and benefits.
And the amount of votes someone gets is proportional to the votes they previously received, so the best vote-getters end up having all of the votes to cast between each other, and everyone else ends up with zero votes.