My guess would be that the word „lying“ implies the intent to claim something untrue, which is hard to prove (not saying this isn’t the case here), opposed to „falsely claiming“ which includes situations where you actually believe what you’re saying even though it’s objectively false.
I‘m not disagreeing with what you’re trying to convey but still: Mussolini very likely never said/wrote that, seems to have been misattributed. IF he did, the Italian word corporazioni, while technically translating to corporations, doesn’t refer to private companies, which in Italian are normally called società.
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