You're right, only the most high-powered people in an organization can get away with terse responses that leave recipients guessing at what their precise intent

You're right, only the most high-powered people in an organization can get away with terse responses that leave recipients guessing at what their precise intent was. "Fluff" is a highly subjective term. What may be fluff for you could be critical signalling for others. Stripping everything down to the bare-bones of what you (or I) may think answers the request sounds intentionally flippant and dismissive. If we fail to address the recipient in a context they understand and share with us that is taken as an offense. With a little effort, however, it is totally possible to be cogent, compact, AND polite.