It is a collection of null results from selected experiments.
That's not an absence of evidence. That's evidence.
If it takes 100,000 "looks" to search the experimental space we only have proof of absense when we have looked at all 100,000. However, I am not going to be easily convinced that after 99,999 looks we don't have something that we can draw a pretty firm tentative conclusion on. If that is now meaningful how about 99,000?
What would you call it if we concluded that the thing is absent after searching one place in an expermental space of unknown size? You can't make conclusions from an absence unless you know how much of the whole that absence represents.
Which is to say that I totally agree with you. But what you're saying is different than what DNA is saying.