Answer

It is possible that the Holy One, blessed be He, told him to write his own words, but that would explain only why the words are holy, not why they are precise and true in every detail, such that one can expound them and infer from them. The opposite possibility is that from the outset Moses said them in God’s name or by divine communication (perhaps in his own style, like every prophet—as the Sages said, no two prophets prophesy in the same style). The writing is of things that were originally said through divine inspiration.
In any case, these are at least prophetic words, and therefore they possess holiness and one can infer from them, even if they were not spoken directly by God. As is known, there are different ways of relating to the Book of Deuteronomy as opposed to the other books of the Torah (for example, the hermeneutic of juxtaposed passages, about which the tannaim disagreed). I seem to recall an article by Rabbi Moshe Pinchuk in Alon Shevut – Graduates that deals with exactly this.
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Questioner:
I seem to recall that it is written that Moses our Rabbi wrote the entire Torah word for word according to God. Is there indeed a source for this in the words of the Sages?
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Rabbi:
There is the discussion about the last eight verses—whether Moses wrote them or Joshua did, and whether Moses wrote them from the mouth of the Holy One, blessed be He, in tears. It is clear that all the rest was written by Moses according to God. See the whole discussion in Bava Batra 15a, and for example in this passage (especially the bolded section):
The Master said: Joshua wrote his book and the last eight verses of the Torah. This supports the one who says: Joshua wrote the last eight verses of the Torah, as it was taught: “So Moses the servant of the Lord died there”—is it possible that Moses was alive and wrote “So Moses died there”? Rather, up to this point Moses wrote, and from here on Joshua wrote; these are the words of Rabbi Judah, and some say Rabbi Nehemiah. Rabbi Shimon said to him: Is it possible that a Torah scroll would be lacking even one letter, when it is written: “Take this book of the Torah”? Rather, up to this point the Holy One, blessed be He, would speak and Moses would say and write, and from here on the Holy One, blessed be He, would speak and Moses would write in tears, as it says elsewhere: “At his dictation he would read to me all these words, and I would write them in the book with ink.”
 
And likewise in the laws of conversion: one who says that even one letter or one law is not from Moses is not a convert.
 
I assume there is much more.
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Questioner:
Thank you for the source, yes, you reminded me.
But I still do not see a source for this in the Torah itself. Heaven forbid, I am not doubting it, but I am interested to know how this was so obvious to the Sages. Did they learn it from reasoning alone (I would be glad to know what that reasoning is), or is this a received tradition, or perhaps I simply did not understand correctly and there is actually an explicit verse about it?
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Rabbi:
I do not know where the Sages learned this from, but if I myself argue that it is not necessarily correct, then obviously I cannot explain where that position comes from. I can only conjecture that this is not a tradition from Sinai, because if it were, I would have to accept it. It also cannot really be tradition, because tradition can only say that the Torah was given at Sinai, but it cannot say what exactly that “Torah” is—that is, whether it is what we call the Torah. There is always the concern that what we have is not what that tradition is referring to. So the possibility of tradition is not really relevant here. That leaves the reasoning of the Sages, or a tradition in their hands that is open to the claim of corruptions.
In my opinion, the Torah itself is not supposed to say something like this. It could be one of its obvious assumptions. The Torah does not necessarily take into account the need to deal with future challenges. It does not have polemical aims.