Why is Miriam accused of sinning when she clearly was only trying to help her sister-in-law?

 Bamidbar (12:1) וַתְּדַבֵּ֨ר מִרְיָ֤ם וְאַהֲרֹן֙ בְּמֹשֶׁ֔ה עַל־אֹד֛וֹת הָאִשָּׁ֥ה הַכֻּשִׁ֖ית אֲשֶׁ֣ר לָקָ֑ח כִּֽי־אִשָּׁ֥ה כֻשִׁ֖ית לָקָֽח׃

Ramban (Bamidbar 12:3) NOW THE MAN MOSES WAS VERY MEEK. This [is stated] to tell us that G-d Himself was zealous for Moses’ sake on account of his [great] humility, since he would never pay attention to injustice [meted out to him] even if he were to consider it such [and therefore G-d vindicated his innocence]. And Rabbi Abraham ibn Ezra explained [the meaning of this phrase] by saying that Moses never sought superiority over any person, nor did he ever pride himself at all about his high position, and certainly not in relation to his brother, thus they [Miriam and Aaron] sinned by speaking against him for no reason.The slander was in connection with Moses’ separating himself from his wife, which Miriam and Aaron attributed to his pride, as if to show that he was a holy man. “We also receive Divine revelations,” they said, “and yet continue our conjugal life.” But in the Sifre [it is said]:Sifre Beha’alothcha 100. “Rabbi Nathan says: They spoke against Moses even in his presence, as it is said, And the Eternal heard it. Now the man Moses was very meek,Verses 2-3. and he restrained himself about the matter.” [According to the Sifre, therefore, Scripture] mentions Moses’ meekness in that he endured [their insult] and did not answer them back, and that G-d was [therefore] zealous for his sake. 

Chofetz Chaim (Devarim 24:9): "Remember what the L-rd your G-d did to Miriam on the way when you went out of Egypt." The Torah exhorted us hereby that we mention verbally, always, the great punishment [leprosy] that the Blessed Lrd brought upon the tzadeketh, Miriam the prophetess — who spoke only about her brother, whom she loved as her soul...she did not speak in denigration of him, but only compared him to other prophets. And she did not speak so to his face to shame him, and not in public, but only to her brother Aaron, privately. And he [Moses] was not offended by all this, but in spite of which all her good deeds did not avail her and she was punished with leprosy for this. How much more so will other people, the fools, who are prolix in speaking "great and awesome things" against their friends, be severely punished for this. 

 Rashi (Bamidbar 12:8) Mouth to mouth I have spoken with him— I have Myself told him to separate from his wife. And where did I tell him this? On Sinai, when I said to him, (Devarim 27-28) “Go, say to to the people, ‘Get you into your tents (rejoin your wives). But as for you, remain you here by Me, and I will speak to you’”