So, I'm missing something from here: be a leader. Lead. When CFO-guy starts telling people you're grooming him for COO, you'll have to reply that, no, you're not (unless you are, but it doesn't appear so in the article). CFO-guy will be let known that the leadership skills shown in his recent actions clearly shows that he's not mature enough to be the COO. But most likely, if you're a leader, he'd know not to tell people he's being groomed unless he knows that's the case and knows you'll agree with him letting people know.
A very real path to lots of politics is creating a power void for others to navigate in by not acknowledging and respect the power you have.
The problem is that it's more like the old telephone game. The CFO might not have explicitly told anyone else that he/she is being told that they're being groomed for the COO, but by the time it gets around the grapevine that could very well be what comes out.