But imagine this scenario: I'm running for office, and I opt in to the matching funds program. All well and good. But then, some extremely well-funded organization, which is totally separate from me and my campaign, spends lots of money glorifying me or denigrating my opponent.
You might argue that there's no corruption here, because I never had direct dealings with that organization, or the people funding it. But the potential for corruption is still there. Once these organizations exist, it will be clear to every candidate what he or she must do to win their favor. Politicians will have an incentive to advance these organizations' agendas, even if the politicians and the organizations never talk to each other. Further, it is quite possible (and indeed probable) that some politicians would cheat and deal directly with such organizations, even if doing so violated campaign finance laws.
You might argue that there's no corruption here, because I never had direct dealings with that organization, or the people funding it. But the potential for corruption is still there. Once these organizations exist, it will be clear to every candidate what he or she must do to win their favor. Politicians will have an incentive to advance these organizations' agendas, even if the politicians and the organizations never talk to each other. Further, it is quite possible (and indeed probable) that some politicians would cheat and deal directly with such organizations, even if doing so violated campaign finance laws.