The fact that you haven't seen a tiger in your trashcan is, however, evidence that there is no tiger in your trashcan.

Edit: Which I think is more or less harmonious with your original post. It appears to me, however, that at some step in the discussion, there was a leap of levels from "absence of evidence for goblins in the trashcan is evidence of absence of goblins from the trashcan" to "absence of evidence for goblins in the trashcan is evidence for the complete nonexistence of goblins".