By several accounts Mussolini gave that speech, but it's not clear that the translation/interpretation is correct though:
A 1938 English book by (anti-fascist author) Gaetano Salvemini translated & interpreted the meaning of that as
In March 1934 Mussolini had to admit that "three-quarters of the
Italian economic system, both industrial and agricultural," required support from the Government if it was not to undergo a general collapse.
Salvemini was teaching at Harvard by 1934 so he was probably fluent enough in English to express what he meant/underwood.
The Economist also commented/paraphrased in 1934 (June 9) on this speech/claim saying:
At the present moment, the State is giving aid, through the I.R.I., to three-fourths of the Italian industrial and agricultural economy. Signor Mussolini here refers to the big banks and big businesses, not to medium or small-sized firms. If he chose, he adds, he could turn State capitalist or State Socialist. But it would be the fault of the capitalists and bankers and financiers, not the fruit of his own will.
The Italian correspondent for The Economist at the time was Luigi Einaudi.
Some Italian authors did interpret the Mussolini speech as claim of actually control (at the time) by the state, but also say that this was factually far from the truth; Antonio Jannazzo in Il liberalismo italiano del Novecento, pp. 148-149 gives the Mussolini claim that interpretation (of actual control) but only to disprove it, saying that while the state was involved in 44.15% of enterprises, it only had a controlling share in 17.8% of them. (These percentages are the capital share of these enterprises of the total economy rather than number of enterprises.) For this fact Jannazzo is citing a 1995 study by S. La Francesa on the Italian interwar economy.
Roberto Bonuglia in Tra economia e politica (p. 92) also gives the Mussolini speech the interpretation of actual state control, but also says Mussolini was exaggerating. Actually Bonuglia is not saying that himself, but quoting (approvingly) an analysis from R. de Felice, Mussolini il duce, vol I, p. 179.
So I think a more metaphoric interpretation of "are on the arms of the state" (the literal translation of "sono sulle braccia dello Stato") is warranted. Or if we take that expression to mean state control ("in the arms" should be "nelle braccia", FWIW) then Mussolini had a major case of truthiness as far as the actual percentage, according to the analyses I found.