Being busy means being occupied or preoccupied. Business means other things are in the way of what we want to do. It is negocio, or the negation of otium or leisure. Scholarly writing is best conceived as a kind of leisure: the mind needs space in which to work. It cannot be pre-occupied by other matters.
So the ordinary guy in the street who complains that professors are lazy is correct. We put our energy into extra tasks to avoid the work that is not really work. Research is either so hard that we would do anything else to avoid it, or so easy and pleasurable that it produces guilt.