A smaller bank I was at had a media policy which was also in the Business Continuity.
It listed Pres/CEO, Chairman, Director of Marketing could speak to the media. There was also a caveat that local media (TV/Radio/Newspaper), could interview others as subject matter experts - i.e. mortgage loan officer discussing getting a mortgage loan, as long as it was in generalities, and not about bank products.
Integrity. With it, nothing else matters. Without it, nothing else matters.