"Would you say that as long as this principle is not falsified, its application is ... what? Nonsense? Dangerous?"

Potentially true. Also, we are people, not formulae, so we have biases, make assumptions, and take leaps of faith. Sometimes even dream.

"Because according to that logic, every scientific statement will be falsified at some point."

Correct. That is actually what I believe is the case. What we know, what little we have tested and managed to eke out, is all only partially true at best, and all of it will change in time. All we can do in the present is the best we can with what we have, as imperfect as it may be. The scientific method is to make a hypothesis about an event that can be tested. Test the hypothesis and then proceed to discard it if it is falsified by the test, or devise more tests and see if you can falsify it. By this process we can gain a lot of confidence in a particular hypothesis that survives a lot of different tests. This is what heart surgeons rely on when hacking and slashing at people. When they're faced with something anomalous, such as not infrequently happens because people have some variations in how things are arranged internally, good surgeons do the best they can to use their experience to devise a solution in real time. But surgery is a lot different than theology. Different treatments can be statistically tracked to see which of them are better, if any are. This just isn't potential to theology.

Theology, I have tried to point out, isn't prone to being tested. Is Wotan the Allfather or is Yahweh? Allah? Raven? What's the point of theology when you can't falsify Raven, or Tengri, as the creator God? Whatever a theologian is teaching is being refuted right now, by hundreds of other faiths, not just sometime in the future. Yet, each of the different faiths also undergoes changes internally. Many Christian sects have radically changed in recent decades, now allowing women pastors, gay marriages, perhaps none so dramatically as Catholicism in that way just this year. Religion is utterly malleable and not infrequently used by pathological scammers to defraud people, because it is untestable, so I am loathe to invest much confidence in any particulars of a given theology. This was not always the case, however, and I was ordained in the ULC many years ago, when I thought I knew God.

I learned later that the more I know, the more I know how little I know, and gave it up for Lent (please forgive my little Lent joke). One thing I have noticed is that almost all true believers just happened to be born where their true religion was the dominant faith. What luck!