No, we define it one way. It is you who deliberately mix up infallibility and impeccability - which are two completely different concepts.
It almost seems like Roman Catholics are threatened by the fact that their Popes are sinful, and that some were especially evil men, as though somehow that fact diminishes the sacred seat of Peter and the legitimacy of Papal procession.
Nice psychobabble.
First, all Popes are by definition sinners, and can never be anything else but sinners.
Second, no Pope can credibly be described as an "especially evil" man - the entire point of this propaganda exercise is to take the actual transgressions of medieval Popes (susceptibility to bribes, having had girlfriends in their younger days, encouraging rather than defusing confrontations for their own gain) and transform them into mind-blowing transgressions like maternal incest, graverobbing, pandering, murder, forcible rape, devil worship, etc.
Third, while there have been Popes who have dishonored their office, Catholics know that the office is distinct from its holders. Popes like Gregory VII are admired precisely for their reforming zeal.
And if one protests these slanders, they're labeled discontented Romanists.
That kind of sneering hatred is worthy of the Obama movement.