I love it when people correct themselves. Saves me the trouble!
You made a good point, though, that the line is also not as clear-cut when you're discussing correlation and causation (e.g., there may be a study to show there is no link between X and Y). However, in such cases "no link" is in fact a positive assertion (the difference between "I don't believe in god" and "I believe there is no god"). Still, even in those cases the only evidence the study is using is absence of evidence.