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Answer: Dealing with skipping berachot of Shemoneh Esrei is the subject of a machloket between Amora’im and apparently Rishonim. Rav Huna (Berachot 34a) says that when one makes a significant mistake during any of the sections of Shemoneh Esrei (first three; next thirteen; final three), he returns to the beginning of the section. Rav Asi agrees regarding the first and last sections, but regarding the middle one, he does not require going back to the beginning (Ata Chonen). He expresses his opinion as follows: "The middle ones have no order," and the Rishonim accept the opinion of Rav Asi. (In your case, either way he had to return to Ata Chonen, which is the one he skipped).

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Tosafot (ad loc.) disagrees, and says that after going back to the beracha he skipped, he continues straight from there, even though it means that he will repeat whatever he recited between making the mistake and discovering it. In the example above, after going back to #6, he continues with #7 and continues forward, thereby reciting #7 and #8 twice. Tosafot posits that the importance of saying the berachot in order is important enough to justify repeating berachot. We are used to repeating berachot when something was done wrong the first time. If one forgot something, for example, Ya’aleh V’yavo, he goes back to R’tzei and continues straight. In your case, the chazan should have recited R’ei another time.
Tosafot deals with the language of the gemara by saying that the lack of order is only in comparison to the halacha found regarding the first and last berachot. While there, one has to go back to the beginning of the set, this is not necessary in the middle ones (rather, one starts with the one he skipped). Tosafot bring a strong proof that the order of all the berachot is important. The mishna (Megilla 17a) says that if one read Megillat Esther out of order, he does not fulfill that mitzva; the gemara says that the same is true for Hallel, Kri’at Shema, and tefilla. This indicates that this is an absolute requirement even b’dieved and therefore justifies repetition to get the order back in synch. (One does not have to go back to the beginning of Shemoneh Esrei, but rather ignores the berachot already recited out of order.) Indeed, the gemara (Megilla 17b) says that Anshei Knesset Hagedola instituted eighteen berachot "al haseder" (according to an order). The gemara then goes on to bring p’sukim to show the logic of each beracha following the one before it. There are other sets of berachot regarding which the order is not critical, such as most of the sheva berachot (see Ba’er Heitev, Even Ha’ezer 62:1) and Birchot Hashachar (Mishna Berura 46:20).
The Shulchan Aruch (Orach Chayim 119:3) follows the predominant opinion of the Rishonim like Tosafot. Therefore, the chazan in question did the wrong thing. Had this been realized any time during chazarat hashatz, he should have returned to R’ei and continued from there.

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