We Jews can say this only because of something that happened within Christianity around the turn of the third century CE. It was then that the fathers of the church rejected the arguments of Marcion, who wanted to jettison the Hebrew Bible as Christian scripture, and accepted the arguments of Tertullian, who wanted to preserve the Hebrew Bible as proof of the ancient lineage of Christianity, and of Jesus as the prophesied savior. As a result of this, roughly a billion Christians today read the Old Testament (as they call the Hebrew Bible) and can be as thrilled when the Qumran scrolls were discovered as the descendents of the Israelites were. But if Marcion instead of Tertullian had prevailed, the Christian Bible would have consisted of the Gospel of Luke and some of the Epistles of Paul, and King David and Isaiah the Prophet would be known only by a few million adherents to an ancient "cult" and perhaps a few thousand scholars and antiquarians.

While you are right in most respects, the history of Israel is a major part of ancient Middle Eastern history and would be studied as part of our general historical education for its own merits aside from any religious significance.

The rise and fall of Israel, like that of Egypt, the Hittitte confederacy, Assyria, and Persia are part of the story of civilization, and given ancient Israel's strategic location in the lower Levant, Israel's significance was pretty much assured from the time of ancient Israel's formation.

While independent (non-Biblical) references regarding King David are hard to come by, there is evidence that Israel was a major military power and Egyptian ally prior to the rise of the Neo-Assyrian Empire, and I suspect his name would be known today in secular circles.

Off topic, but I think its a good thing that the arguments of
Marcion were rejected. It would have been even more disastorous
for the Jews if Christans saw us as worshiping the demiurge.