... Your "correction" is circular: ...
Nope. Tautological maybe but not circular. The absence of evidence for "X" does not mean "X" does not exist, just that evidence for it has not been found/discovered (yet).
... Not very useful.
Curiously, I find it more useful to be clear on the logic rather than skip a step. That's why I added "known" to the syllogism.
You can probably think of a few things that used to be unevidenced but that are now known.
Enjoy