Hashem testing you with false signs, or is this just dibra Torah kilshon bnei Adam?

Summary: The Torah indicates that the signs of a false prophet of idolatry are really simply Hashem testing you, which seemingly indicates that the signs are real, and that Hashem would mislead in this way. While theologically possible, is this indeed so? Ibn Caspi gives another way, in which this is a (near-) false statement in the Torah, for the hamon am who would not otherwise understand.

Post: In Devarim 13, in parashat Reeh, we read:

2. If there will arise among you a prophet, or a dreamer of a dream, and he gives you a sign or a wonder,		ב. כִּי יָקוּם בְּקִרְבְּךָ נָבִיא אוֹ חֹלֵם חֲלוֹם וְנָתַן אֵלֶיךָ אוֹת אוֹ מוֹפֵת:
3. and the sign or the wonder of which he spoke to you happens, [and he] says, "Let us go after other gods which you have not known, and let us worship them,"		ג. וּבָא הָאוֹת וְהַמּוֹפֵת אֲשֶׁר דִּבֶּר אֵלֶיךָ לֵאמֹר נֵלְכָה אַחֲרֵי אֱ־לֹהִים אֲחֵרִים אֲשֶׁר לֹא יְדַעְתָּם וְנָעָבְדֵם:
4. you shall not heed the words of that prophet, or that dreamer of a dream; for the Lord, your God, is testing you, to know whether you really love the Lord, your God, with all your heart and with all your soul.		ד. לֹא תִשְׁמַע אֶל דִּבְרֵי הַנָּבִיא הַהוּא אוֹ אֶל חוֹלֵם הַחֲלוֹם הַהוּא כִּי מְנַסֶּה יְ־הֹוָ־ה אֱלֹהֵיכֶם אֶתְכֶם לָדַעַת הֲיִשְׁכֶם אֹהֲבִים אֶת יְ־הֹוָ־ה אֱלֹהֵיכֶם בְּכָל לְבַבְכֶם וּבְכָל נַפְשְׁכֶם:

A 'sign' or a 'wonder' (pasuk 3) would seem to indicate predicted future or a miraculous event. This would then indicate that the false prophet can work miracles, and / or predict the future. How? Hashem is helping this work out, in order to test you, as the false prophet uses this to prove the existence and power of other gods.

This seems rather theologically strange, that Hashem would do this. But I see how this can be justified -- that this is a test to see if you are truly committed. Knowing it is a test, because of this pasuk, might spoil some aspect of the test. After all, if you know that this is really Hashem empowering the prophet, then the false prophet bringing signs or wonders is not such great proof of his own deity's existence or power. Though the test might now be whether to believe the Torah or the prophet.

At any rate, despite this being the simple implication of the pasuk, Ibn Caspi rejects this. He writes:

Of course it isn't Hashem that is doing this to trick you! Rather, the false prophet accomplishes this using whatever mechanisms he uses to generate the miracle or the sign. Hashem isn't causing this.

However, the ignorant masses -- you know, the type who are persuaded by Rav Amnon Yitzchak -- will believe this sign, and will not be able to see to the heart of the matter. Therefore, the Torah delivers a sort of falsehood that the hamon am will be able to understand. Treat it as a decree of the king not to listen to this "miracle" worker. And because of their feeble intellect, He gives them a good reason which is fitting for them, that Hashem is "testing them". And this false reason is not strictly false, for after all, Hashem is the First Cause.

This fits in well with Ibn Caspi's general application of his particular extension of the idea of dibra Torah kilshon benei Adam. Though Ibn Caspi does not use that technical term here.