1. I suspect you'd have "protection" to use your title as a credential in a relevant professional forum.
2. Most companies also have policies on running for public office, usually because of legal oversight to public procurement or policymaking.
3. Neither of your examples are explicitly "to the media", which is being discussed here.
4. Most companies are thrilled to help you advance your cause and theirs in things like running for public office or industry leadership, and will give you great resources like media training.
5. Straw-men: I bet the company would care if you were running on a policy platform of reducing sanitation in minority neighborhoods, or speaking at a KKK rally.
If these activities have nothing to do with work, then why are you bringing work into it? And if you're bringing work into it, then it doesn't strike me as unreasonable to tell your company about it.
It's not about "being afraid to talk to the press"... that's my point.