Deborah, you're right on. But social media manager is just another word for inhouse agency.
Since social media is but one of various media to promote the brand, possibly the most exciting, it is the responsibility of the CEO to identify and identify with the voice of the brand, mainly because the brand is the most important asset of a company. We can indeed say that the CEO is the brand.
Whoever speaks for the brand in headlines or in tweets better understands longterm strategic positioning, not a task for the churring, mumbling, whining, snorting, hissing and tail slapping sounds of inhouse beavers, but the task of account and media planners and their copywriters at professional ad agencies.
All this twittering and social media sputtering is just another charming cloak on a selfish motive, advertising under an assumed name. After all, advertising headline writers have been trying to be social for years.