So if Buddhism does not assert that it is the One True Path, what's the Fourth Noble Truth?
The hand pointing to the moon is not the moon.
``Come, Salha, do not be satisfied with hearsay or with tradition or with legendary lore or with what has come down in scriptures or with conjecture or with logical inference or with weighing evidence or with a liking for a view after pondering it or with someone else's ability or with the thought 'The monk is our teacher.' When you know in yourself 'These things are unprofitable, liable to censure, condemned by the wise, being adopted and put into effect, they lead to harm and suffering,' then you should abandon them.''
The Buddha is saying not to follow something on the basis of externals, but rather on one's own self testing. That the Buddha arrived at the Four Noble Truths and the Eightfold Path through such testing is of importance.
If we return to the Pali scriptures, we can see that although the Buddha states that the question of God/gods is in the realm of "unanswerable questions," that even if they did exist they would ultimately undergo death and rebirth, albeit perhaps in an unimaginably long time frame from the perspective of humans. He considers debates over deities pointless, _because even they are subject to the truths he espouses_. Is this not a truth claim that contradicts most theistic religions? Is this not a truth claim to the supersession of Buddhist truth over others? (Forgive me, but my copy is in another location so I can't give an exact reference.)
Although the view of deities in Buddhism differs between schools, the general understanding of Buddhism is that such belief is not conducive to enlightenment. This is indeed an exclusivist truth claim to the superiority of the Buddhist practice.
"The pointing finger is not the moon" has never, IME, been taken to make ontological claims of any kind about the moon, except that it's not the finger pointed at it. It means the same thing as, "The map is not the territory," and not, "Because this map shows rivers and towns in these locations, such rivers and towns must exist."
Your idea of a thing is simply and solely your idea of the thing; the thing, itself, is simply and solely the thing, itself. Buddhism just suggests out that you conflate them at your peril (to the extent, of course, that Buddhism has a notion of "peril").
The hand pointing to the moon is not the moon.
``Come, Salha, do not be satisfied with hearsay or with tradition or with legendary lore or with what has come down in scriptures or with conjecture or with logical inference or with weighing evidence or with a liking for a view after pondering it or with someone else's ability or with the thought 'The monk is our teacher.' When you know in yourself 'These things are unprofitable, liable to censure, condemned by the wise, being adopted and put into effect, they lead to harm and suffering,' then you should abandon them.''
AN 3.66