ITT: People argue semantics. How about we replace "passive" with "secret"? (You could also replace "Passive Check™" with "a check that is passively done")
If if is done manually, it is an active check. If it happens automatically, it is a [secret] check.
The title changes to
We shouldn't be notified of failed [secret] checks (especially perception)
In which case the title becomes a tautology. Obviously we shouldn't be notified of secret checks because, by definition, they are secret. Unless we succeed at the check, in which case the game should of course tell us what we noticed.
Prof. Dr. Dr. Mad S. Tist 
