Woody Allen is guilty of ugly, thoughtless behavior, and for that reason many consider him guilty of molesting his daughter; some of the "evidence" for this guilt offered in this thread (a fictional movie Allen made and the belief of an otherwise admirable family member, whom an older sibling has said was groomed by their mother by age four to think the worst of Allen) are at best cherry-picked (the opinion of Moses Farrow that the accusation of molestation is preposterous being omitted).
But to the thread's point:
Many competition poets
(see Chris O'Carroll below his poem here) don't consider poems written to order--even very good ones, even ones they spend a lot of time writing, even ones that bring them far-and-away the majority of the money they earn through poetry--to be "real" poems.
This points to an important distinction between poetry and plumbing or teaching. Unlike (other) professions, to write poetry requires inspiration, and, for most, inspiration lies at least partly beyond control.
Whether people consider themselves poets when not inspired may depend on whether they believe that the next inspiration, or the between-inspiration growth James mentions are nurtured by feeling like poets. It's just as reasonable to believe feeling like a poet eliminates an incentive to find inspiration. A matter, I suppose, of temperament.