That's not a part of science
If any particular scientist has made that claim, he doesn't speak for the collective, and he is making a claim to knowledge that others realize that he cannot possibly possess.
The claim of rational skeptics is that no idea should be believed without testing it against reason and reality. If we can't detect it even in principle because it has no impact on reality, then its existence is irrelevant.
And how do we know that what we don't know, because we can't detect it, doesn't have impact on reality and is irrelevant? We only can test things to the extent that we have capability to do so. The gradual unfolding of science has been a growing awareness that things we once assumed did not have impact on reality do. That we don't know it doesn't mean it doesn't exist or is irrelevant.
I can think of the combustion of carbon, for one, which is such big news for us today. Back in the 1896 when Svante Arrhenius first proposed that carbon released into the atmosphere would cause temperatures to warm, most rational skeptics felt that its existence was irrelevant. Yet it was tremendously relevant to the decisions that people and governments were making at a time the human population was transitioning to fossil fuels in the impacts this would have on not only the lives of their descendants but on just about every aspect of the ecosphere.
Another is agricultural chemicals. Such a view that things are irrelevant as long as we are unable to observe them has led to the pouring of millions of tons of agroindustrial chemicals all over the surface of the planet, which which we are finding is having a myriad of effects, biochemical, ecological, and social. Insects and birds are disappearing just as Rachel Carsons predicted, humans are getting all kinds of cancers and diet related diseases that didn't exist just some decades ago, fertility of soil is being used up faster than ever before, species populations are being devastated, and due to changes in scale of production forced on agricultural producers, there has been vast removal of population from the countryside globally on a scale unprecedented in the history of agricultural societies with barely any though that perhaps something might be wrong with this. Most rational scientists and even many anthropologists have little appreciation for the relevance this all has for our future, not even because it hasn't been observed.
Another position we heard from supposedly rational scientists no more than a decade or so ago was that genetic engineering wouldn't have effect on us for various reasons -- that it was just an extension of nature, that relevant enzymes aren't produced by humans, that the associated herbicide is sticky and doesn't leave the soil that it was sprayed on, that it is not absorbed by animals that eat it. On all counts recent studies are proving these assertions wrong. Just one scientist at MIT has written 80 or more papers giving evidence of strong ties between Glyphosate and the exploding rates of autism, Alzheimer and other diseases, with demonstration of the mechanisms causing it. Manufacturers said that it would have no effect on humans because our bodies don't produce the enzyme it suppresses, but our gut flora do produce that enzyme and it turns out it is essential to many systems of the body including cleaning the brain of wastes, according to the scientist. And then are not the ecosystems that it is being applied to of relevance to us? These are all things that weren't observable but they are turning out to be having immense relevance. Many scientists were calling for caution based on "rational" deductions from other knowledge as well as the cautionary principle, but it was the prediction of the harmlessness without any means to test things that hadn't occurred yet that were used to justify policy -- evidently by 'rational' scientists, or to put it another way practitioners who referred to science to convince people that they were rational. Furthermore, resulting reduction of diversity in crops as the GM crops are pushing out local varieties of both domestic and wild versions of crops are threatening to have catastrophic consequences--this too was predicted through rational deduction and induction. Many elements furthermore have been long observed and well documented for hybrids and their associated packages of chemicals and technology.
Your use of the word "rational" with the word "science" is contradiction in terms, since science, due to the close association of rationalism with a religion which the Roman Church was using to attack the emerging sciences back in the middle of the last millennium, discarded rationalism for an empiricism that presumed that the only real things are those we can detect, as you say. It is almost as if you are quoting Decartes and his epigones directly, it has so much infiltrated into our thought.
And yet, the premises that this position bases itself has no empirical basis and must be taken on belief. Alfred Whitehead discusses this in his book
Science and the Modern World. He also points out that the language science uses originates from previous vernacular usages makes scientific knowlege imperfect representations of the world which, combined with premises such as the one above, make it impossible for science to actually reach truth.
Regarding Whitehead's criticism of science for premising itself on unverified beliefs, Karl Popper recently said basically the same thing when he argued that our sciences extend from paradigms which make them valid only as long as the paradigms hold up. A good example of changing premises or paradigms are Einstein's theory of relativity and Max Planck's quantum mechanics which, as Whitehead points out, despite their revolutionary implications for all human thought and culture still have not been integrated into most of the sciences, which simply go on as if Einstein and Planck never existed. Creating a premise for science that extended from these revolutionary changes was in fact the work of the last several decades of Whitehead's work.
The scientific method always selects particular elements of things as significant and in doing so discards other elements that may be significant: for example, the thought that we can know a living thing by describing it. This leads us to be indifferent of other properties that organisms and things have in our appropriation of them. A good example is the hunting whales for oil. While remaining indifferent to their role in the ecosystem which at that time was not understood and thus considered irrelevant to the human use of whales as a means of harvesting carbon energy. Whales it turns out caused up-welling of lower sediments from the bottom of the ocean, and their great reduction has caused changes in the ecology and productivity of the entire ocean, with implications furthermore for another problem we are having, climate change. Also, after whale populations were reduced, marine mammals region by region have been disappearing as killer whales which once preyed on whales now have been forced to shift to eating one population of marine animals after the other to make up for the very small proportion of whales they once hunted to sustain their population.
Finally, growing means to control increasingly powerful forces has given us the ability to have increasingly wider effects on our world without even knowing what effects we are having until they come about. There are many, many things being disclosed which we previously could not detect, or which we failed to anticipate because our premises led us not to ask the right questions. And yet I would say that no rational person would say that they are irrelevant to us just because we are unable to detect them. Unfortunately, there are plenty of irrational people yet who are saying that things are irrelevant even when we do detect and analyze them in detail. Alfred Whitehead would say our dangerous mistake is to assume that just because we don't have the means to detect something, or because our knowledge is incomplete, that what we don't know is irrelevant to us. He gave this warning, furthermore, nearly a century ago.