I do not understand what is the mechanism that equates "more people voting" with "less money influence". You have done little to explain it, only using an argument from authority ("An important man said it, therefore it's true").

"Big money" isn't directly buying votes. Increasing the number of votes doesn't make an election "more expensive" to buy. If you have only three candidates, to buy out their loyalty you need the same amount of money, regardless if you have one million of people voting for them or ten.

Direct democracy renders the process even worse. People cannot be fully informed about all topics at all times - I hope you realize how uncontroversial this opinion is. So they'll just find the information that is easiest to find and digest and be influenced by it. If you have enough money, you can be the easiest source of information in the topic you care.