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Was the Decima MAS unique in achieving such a high degree of independence outside the RSI authorities 1943-45, or were there any other units who were able to gain this sort of autonomy, even if only for a short period?
Please note that the RSI hasn't been my main area of research, so hopefully others will respond as well.
The challenge to your question is defining the authorities of the RSI. There were several different armed forces under the umbrella of the RSI name (ENR, GNR, Black brigades). X MAS was technically Navy, so already differed from the other military forces due to that fact.
What X MAS actions do you see as exercising independence outside the RSI authority?
Numerous things. The fact that Borghese made his own treaty with the Kriegsmarine after the Cassibile armistice, the fact that Mussolini tried to have Borghese arrested because he resented Borghese's autonomy (and the fact that Decima MAS troops were prepared to march on Salò to free their commander when they heard of this), the fact that Decima MAS members were not required to swear the oath to the Salò regime, that the Decima MAS was able to establish its own auxiliary forces, print its own propaganda, launch some of its own offensive operations without consulting any higher Italian authority than Borghese, etc. etc.
If you read the history of the Decima MAS during the 1943-45 period, you will see that it functioned for a time almost as Borghese's own "private army". The RSI navy (and government) had little direct control over this unit.
The short answer to the opening question is: no.
The longer answer is: the RSI had a chaotic organization where different bodies (the State administration, the Fascist Party and the Germans) were a source of power, often in competition. This competition allowed some units to reach a certain degree of autonomy by merely playing one authority against another one, but none reached the independence of the X^ MAS. At best, playing the card of the German support, the Legione Autonoma Mobile Ettore Muti managed to get a certain freedom of action, but without the support of the public opinion gained by Borghese's men. On the opposite side, we could also take into account those bodies of the pre-armistice State which managed to survive under the RSI, often keeping a good autonomy and secret contacts with the Kingdom, such as the Carabinieri and the Guardia di Finanza.