Honesty compels me to admit that there are times when exactly the wrong person at exactly the wrong time with exactly the wrong motives has nevertheless said exactly the right thing.
Tom Marshall, Understanding Leadership, 1991, p97 (HT: ξἐνος)
Of course, the reverse is also true: There are times when exactly the right person, at exactly the right time, with exactly the right motives, has said exactly the wrong thing. And this version seems to fit my experience better.
“Humankind, bright sparks since BC” (cf. Job 5:7)