It is right to be present on Twitter. But the question is: Should it be the single/primary channel or only secondary channel filled from a primary source, like their website?
Of course, running a website, which allows those quick edits requires with dealing with secure infrastructure, maybe apps dir field agents to write something etc. which they could all outsource to Twitter (and vendors of tools built around Twitter API for scheduled tweets etc.)
Its somewhat similar with public broadcasters (BBC, German ARD etc ) putting their content on YouTube (where consumers are) vs their sites (where they control it, including privacy concerns)