The way you state that seems misleading, even if technically true.
I do not assume that all (or even most, or even many) Quaesitors are corrupt, self-serving bastards. What I do assume is that they are more difficult for a given mage to trust than the other mages in their own covenant.
Every single day 'mage A' can converse with mages B through H (their covenant-mates -- well, except for mage H who we already established is away for a season to study elsewhere). Mage A can know something of their ambitions, goals, motivations, and methods; which books they write, which they read; what lessons about proper behavior they have instilled in (past or current) apprentices; what other folks (magical and otherwise) say about past interactions with all of them; what their attitudes are towards other mages, the Order, the church, mundanes, animals, faeries, and so on.
The Quaesitor is a stranger, a comparative (and perhaps absolute) unknown. Even a high-integrity Dudly Do-Right Quaesitor is handicapped by this.
And a mage who volunteers to sacrifice even as little as a season per year away from their magical pursuits is a little suspect -- how do they intend to keep up with their peers? Is there a short, quick, tempting, easy road to magical power which the Quaesitor is secretly pursuing? If it is so utterly unsurprising and yawn-inducing to discover that a close associate in the same covenant has been keeping Demon-licking secret for years, how much more opportunity for malfeasance does someone outside the covenant have?
I do not treat 'Quaesitor exists, and appears' as an automatic presumption of guilt for everyone else in the covenant. If Dudly Do-Right the Quaesitor shows up at the gates, then how are they to know that I am the only 'good' one in the covenant, and am not neck-deep in the Demon-licking?
Any Quaesitor who shows up uninvited (especially uninvited and in an official capacity) is dangerous, precisely because I may now need to prove that I never did all the things that I never did -- and, because I was busy doing mage-stuff, did not bother to document that I was not involved with all the stuff I did not know about.