They always tended to be as independent as it was possible to be under the circumstances, c.f. Gramsci’s letter to Togliatti. They were in the odd position after the war of having liberated quite a bit of Italy on their own (Genoa, especially, has a strong tradition) before the Allies arrived, and without Soviet assistance. There was also a strong tradition in the South, despite ferocious repression (the Sicilian May Day massacre especially) and, like a lot of western communist parties, they had a very lively cultural life. They also tended to have much more respect for democracy than most of the `bourgeois’ parties.
A great film to get if you can find it is La Cosa, which Nanni Moretti made by filming the discussions in CP branches as the party was heading for its dissolution and split in the early 90s. One member in the Mirafiori branch (so a Fiat worker) asks why they should give up on the sacrifices of the past, including when their shop stewards were murdered by the Red Brigades.
One odd comment I came across a few years in an interview with Giorgio Amendola was that Italian communism always had a Trotskyist tinge because Mussolini banned official communist publications, but it suited him to have Trotsky published, since his denunciations of Stalin sowed confusion amongst the Italian left. Amendola’s view was that most Italian communists of that generation got their history from Trotsky’s account of the Russian revolution because it was all they could lay their hands on.
I think the fact that the PCI effectively had to develop under Fascism, rather than being defeated by it (as in Germany), made a big difference internally and to their support.