The McKinsey Quarterly has just fired a warning shot across the desks of CCOs.

They – and CMOs and CEOs too – better pay attention.

The article, “Rebuilding Corporate Reputations,” (subscription required) describes the dramatic extent to which the events leading up to the current recession have eroded public confidence in corporations.

And it describes the equally dramatic changes in how corporations need to respond: integrating their communications activities, engaging with digital and social media, genuinely changing business practices, stepping up the quality of their research, listening to and activating constituencies, and engaging the CEO with the community.

Good advice – indeed, it’s what we’ve been counseling clients for some time.

But the kicker comes at the end:

“To achieve the necessary coordination,” the article’s final paragraph begins, “a senior executive should be accountable for such efforts. A strong understanding of customers and marketing might make the CMO appropriate to play this role.”

Surprisingly, the article didn’t develop that theme further. And we think that, given the CCO’s experience with “earned” communications, and with such non-marketing communications functions as investor relations, public affairs, and corporate social responsibility, at least as strong an argument can be made for placing the responsibility with the CCO.

But the fact is that you can make the argument either way, and in most companies the contest won’t be resolved by abstract principles. The prize — and the budget — will go to the leader who seizes the opportunity, and who demonstrates the knowledge, the skill with emerging media, the right talent pool, and the creativity, to become the “chief reputation officer.”

If the McKinsey article’s cursory treatment of the question reflects a CEO bias toward CMOs, it’s a warning to CCOs that they better get on the ball or find themselves marginalized.

To CMOs, it’s a warning that they may be expected to show leadership in activities that go way beyond marketing, and for which they may be unprepared.

And for CEOs, it’s a reminder that, as always, they’re ultimately responsible. Before they delegate this responsibility, they must fully appreciate the implications of where, and with whom, they entrust their company’s reputation.

This is a big issue – and we’ll return soon with more POV on McKinsey’s specific recommendations, not just the question of who runs the show.

But for now, you’ve been warned.