How do you define competence? Competence seems like a word that can mean anything, just as long as the job is done. Do you respect certain kinds of competence (ie. coding) more than others (ie. political maneuvering)?
For a politician, being 'competent' might mean, at times, being the most ruthless, machiavellian snake in the room (with the smiling, innocent face of a bunny-rabbit of course) -- because at the end of the day, he's the guy who gets the laws made / votes plugged-in and thus furthers the mission of the party. (and that mission might be an honourable one.)
For an entrepreneur, it might mean being an amazing smooth-talking sales guy (the kind who actually makes sales, not the kind who turns everybody off with an annoying voice) who makes you uncomfortable with the promises he makes, yet allows the company to just-barely-survive through a tough spot.
If a guy starts a web app company and drives it to success by outsourcing the programming offshore, do you respect him less than the guy who codes it himself?
Just curious because you said that somebody can have "apparently achieved great things" yet still display a "severe lack of competence".