Summary
A woman I don't know posed the following question to me while getting a quick ride to her car: It seems that Rashi and Sifrei on Devarim 1:1 say that Moshe said that he himself had punished Miriam. Is this really what the Midrash and Rashi mean? If so, what are we supposed to learn from that?
Background
The first verse of the book of Devarim introduces Moshe's final great speech with a long list of geographical references:
אֵ֣לֶּה הַדְּבָרִ֗ים אֲשֶׁ֨ר דִּבֶּ֤ר מֹשֶׁה֙ אֶל־כָּל־יִשְׂרָאֵ֔ל בְּעֵ֖בֶר הַיַּרְדֵּ֑ן בַּמִּדְבָּ֡ר בָּֽעֲרָבָה֩ מ֨וֹל ס֜וּף בֵּֽין־פָּארָ֧ן וּבֵֽין־תֹּ֛פֶל וְלָבָ֥ן וַחֲצֵרֹ֖ת וְדִ֥י זָהָֽב׃
These are the words that Moses addressed to all Israel on the other side of the Jordan.—Through the wilderness, in the Arabah near Suph, between Paran and Tophel, Laban, Hazeroth, and Di-zahab,
Rashi, channeling various Midrashic teachings, explains that each of these references was actually a veiled criticism of the Israelites. Regarding "Hazeroth," Rashi provides two interpretations, one of which is:
אָמַר לָהֶם הָיָה לָכֶם לִלְמוֹד מִמַּה שֶּׁעָשִׂיתִי לְמִרְיָם בַּחֲצֵרוֹת בִּשְׁבִיל לָשׁוֹן הָרָע, וְאַתֶּם נִדְבַּרְתֶּם בַּמָּקוֹם:
He said to them, “You ought to have taken a lesson from what I did to Miriam at Hazeroth because of the slander she uttered, and yet you even after that spoke against the Omnipresent."
This interpretation is apparently based on Sifrei Devarim 1:15:
אמר להם: לא היה לכם ללמוד ממה שעשיתי למרים בחצרות? אם למרים הצדקת לא נשאתי לה פנים בדין - ק"ו לשאר בני אדם.
He said to them: Should you not have learned from what I did to Miriam in Chatzeroth? If I did not show favoritism in judgment to Miriam the righteous, how much more so (would I not do so) to others!
The incident in question, located in Hazeroth per Bamidbar 11:35, is recounted in Bamidbar 12: After slandering Moshe in conversation with Aharon, Miriam was stricken with tzara'at and banished from the Israelite camp for seven days.
Difficulty
In both Rashi's and Sifrei's renditions of this interpretation, it sounds like Moshe was ascribing the punishment of Miriam to himself. They both say "what I did to Miriam," and the speaker here seems very clearly to be Moshe. After all, the text being interpreted begins "These are the words that Moses addressed ...." This is surprising, since Miriam's primary punishment, tzara'at, was pretty clearly visited upon her by God, as it appeared just as His presence departed after He rebuked her and Aharon. The first and only action Moshe apparently takes in this episode is to pray for Miriam to be healed.
Questions
Did Sifrei and Rashi really mean to say that Moshe was saying that he had punished Miriam himself?
If not, why does it sound that way?
If so, what are Sifrei and Rashi trying to teach us with this surprising ascription?