(א) ודברתם אל הסלע... והקרוב מן הדברים שנאמרו בזה והוא טוב לדחות השואל הם דברי רבינו חננאל שכתב כי החטא הוא אמרם (פסוק י) המן הסלע הזה נוציא לכם מים וראוי שיאמרו יוציא ה' לכם מים כדרך שאמרו (שמות טז ח) בתת ה' לכם בערב בשר לאכול וגו' וכן בכל הנסים יודיעום כי ה' יעשה עמהם להפליא ואולי חשבו העם כי משה ואהרן בחכמתם הוציאו להם מים מן הסלע הזה וזהו לא קדשתם אותי (דברים לב נא)...
And you Shall Speak About the Rock-- ... And the closest of all the things said about this, and which is good to satisfy the questioner, is the opinion of Rabbeinu Chananel, who wrote that the sin is [Moshe's and Aharon's] saying, "Shall we bring out water for you from this rock?" While it was fitting to say, "Hashem will bring out water for you," like they said, "When Hashem gives you, at night, meat to eat..." And so, with all miracles, they informed them that Hashem would deal miraculously with them. And maybe, the people thought that Moshe and Aharon, in their own wisdom, brought out water for them from this specific rock. And this is, "You have not sanctified me."...
החטא הוא אמרם (פסוק י) המן הסלע הזה נוציא לכם מים וראוי שיאמרו יוציא ה' לכם מים כדרך שאמרו (שמות טז ח) בתת ה' לכם בערב בשר לאכול וגו' וכן בכל הנסים יודיעום כי ה' יעשה עמהם להפליא ואולי חשבו העם כי משה ואהרן בחכמתם הוציאו להם מים מן הסלע הזה וזהו לא קדשתם אותי (דברים לב נא)...
(1) The sin consisted in their saying: המן הסלע הזה נוציא לכם מים?, “Are we to extract water for you from this rock?” They should have said instead: יוציא ה' לכם מים, “G’d will extract water for you.” (verse 10). In Exodus 16,8 Moses had been careful to phrase the announcement of the forthcoming phenomenon of manna by attributing it to coming directly from G’d. Similarly, when predicting any of the other miracles which had been announce beforehand, Moses had carefully attributed the miracle to G’d. By failing to do so this time they left the way open for some of the people to think that the water when it would gush forth would be the result of Moses’ and Aaron’s combined knowledge.
This is also the meaning of the words (Moses quoting G’d) לא קדשתם אותי, “you have not sanctified Me” (Deuteronomy 32,51)... In this instance the people did not observe any evidence of G’d’s involvement so that it was easy to conclude, based on Moses’ and Aaron’s phrasing it, that they themselves had initiated this phenomenon.
(13) These are the waters of Meribah, where the children of Israel strove with the LORD, and He was sanctified through them (the water).
While this opinion stands initial scrutiny, and indeed the Ramban calls it sufficient to 'satisfy the questioner', its central point is not lacking a rebuttal.
The Ra"ch is assuming that 'Can we take water out of the rock for you?' is a rhetorical question, whose is answer is yes, as Moshe proceeds to take water out of the rock.
However, this assumption ignores the shadow that the Korach story is casting on Mei Merivah. See here for my contention that our story takes place less than a year after Korach, at the start of Year 3 in the desert; regardless of that argument, the linked source sheet shows how linked the complaints of Korach are to the complaints of the people here in Kadesh.
Think back to takeaway #2 from this sheet. Moshe and Aharon used miracles and wonders to prove themselves in the Korach story, which clearly shows that they are emissaries of G-d-- unless it doesn't. Remember the magicians in Egypt?
(כ) וַיַּֽעֲשׂוּ־כֵן֩ מֹשֶׁ֨ה וְאַהֲרֹ֜ן כַּאֲשֶׁ֣ר ׀ צִוָּ֣ה יְהוָ֗ה וַיָּ֤רֶם בַּמַּטֶּה֙ וַיַּ֤ךְ אֶת־הַמַּ֙יִם֙ אֲשֶׁ֣ר בַּיְאֹ֔ר לְעֵינֵ֣י פַרְעֹ֔ה וּלְעֵינֵ֖י עֲבָדָ֑יו וַיֵּהָֽפְכ֛וּ כָּל־הַמַּ֥יִם אֲשֶׁר־בַּיְאֹ֖ר לְדָֽם׃... (כב) וַיַּֽעֲשׂוּ־כֵ֛ן חַרְטֻמֵּ֥י מִצְרַ֖יִם בְּלָטֵיהֶ֑ם וַיֶּחֱזַ֤ק לֵב־פַּרְעֹה֙ וְלֹא־שָׁמַ֣ע אֲלֵהֶ֔ם כַּאֲשֶׁ֖ר דִּבֶּ֥ר יְהוָֽה׃
(20) And Moses and Aaron did so, as the LORD commanded; and he lifted up the rod, and smote the waters that were in the river, in the sight of Pharaoh, and in the sight of his servants; and all the waters that were in the river were turned to blood... (22) And the magicians of Egypt did in like manner with their secret arts; and Pharaoh’s heart was hardened, and he hearkened not unto them; as the LORD had spoken.
(11) And Moses lifted up his hand, and smote the rock with his rod twice; and water came forth abundantly, and the congregation drank, and their cattle.
The answer to the query, then, is an unequivocal no; on their own, Moshe and Aharon cannot do anything supernatural. They are not magicians. It is G-d who is performing the miracles, G-d who is calling the shots, G-d who is behind Moshe and Aharon. And so, the rhetorical question does not remove Hashem from the equation; just the opposite is true.
If you have questions/comments/counter-arguments, do not hesitate to message me.