He's not wrong, per se, but it's also not a relevant point when the problem becomes immediately unsolvable when you think about it a little more.
Generally, I think that Lessig's work in this area is laudable but misguided: that is, that the influence of money is a symptom and not the root cause he claims it to be. I really hope that he creates positive change as a result of this, but I don't have high expectations.
My belief of what the root cause is is that the citizenry is too used to keeping their heads down and don't have the mental framework to accept the offering of power that democracy is supposed to be. So, in a sense, you can limit the influence of money by decentralizing power to the extent that it is properly a democracy. I would loosely define a democracy, in this context, to be a society in which over 70% of the citizens are active participants in governance.
(That last paragraph was mostly a matter of preemptively responding to "you can't just leave us hanging" charges rather than a proper manifesto.)