"You can't have a fact unless it's falsifiable."
On this particular point, I disagree...
One of these propositions is true, and therefore a fact:
1. Mozart was a better composer than Bach.
2. Bach was a better composer than Mozart.
3. Either Mozart or Bach was a better composer than a given randomly-selected High School band student.
None of these are falsifiable. There is no objective test for them, as musical taste is (insofar as we are aware) not scientifically resolvable.
To be clear, though, outside of that, my post was -meant- to agree with and summarize the broader content of your post. You apparently understand the difference between "not scientific" and "anti-scientific" better than most "pro-science" people, including scientists, do, or are willing to be honest about. And you also have a much more real-world awareness of the fact that many subject domains aren't addressable by scientific method, yet people still validly hold that there are ultimately ideas that are true within them, regardless of formal testability--politics and economics, to name a couple.
The recent Dawkins/Hitchens/Tyson/etc. movement to cast every human endeavor within the context of scientific method, and judge everything on that basis, is really a rehash of the philosophically-dead Logical Positivism movement. It doesn't work, and it can't work. And I don't think we have any fundamental disagreement.