The answer can be broken into two parts, that being politically and culturally.

Before we get to that, I want to briefly address the point you brought up about the concentration camps in Italy as it offers a unique window into what war was like inside of Italy. The Italy that was at war was not completely united behind the cause the Fascists preached, and featured the first hint that the yoke around the neck of the people was not one of consensus. The Italian military (with the assistance of the Nazi apparatus) carried out atrocities in the Dalmatians that is not up for debate, but this was not the fate of those repressed internally. The concentration camps for repressed people (Jews, Slavs, antifascists, et al) were a far cry from the horrors of the Shoah. As one survivor of German and Italian camps explained about the Italian camps,

“Life in this camp was like in an oasis ... we felt fully protected. We were completely free within the camp … Whenever we asked the authorities we got; for instance, they built a gangway from the barracks to the latrine so during the winter when it was cold we wouldn't catch cold. They supplied us with food and during the winter they even supplied us with military clothing, medicaments, whatever was needed. They even permitted us and assisted us in setting up a grade school and a high school within the camp … We had musical evenings in the camp to which officers came, Italian officers and soldiers from the entire area. It was a very pleasant life in the camp.”

This is not to say that the camps outside of Italy were a different matter. These were camps of repression - per scopi repress - and they were as brutal as those that the Nazis engineered. Also, once Italy ended their alliance with Germany and most of Italy fell under a puppet regime of the Nazis all of the camps in Italy became brutal experiences. This distinction between what was considered under Italy, and what was considered under Germany is an important distinction in answering this question as well.

##Political Blame

First, it is easy to contest the notion that Italy did not get any blame for World War Two. The Paris Peace Treaties in 1947 explicitly laid out Italy to be an aggressor state and a holder of the blame:

Whereas Italy under the Fascist regime became a party to the Tripartite Pact with Germany and Japan, undertook a war of aggression and thereby provoked a state of war with all the Allied and Associated Powers and with other United Nations, and bears her share of responsibility for the war,

In addition to this there were the punitive aspects of the Treaty. It was not a kind treaty by any means - even though the Western Allies forwent any reparations (we will get to that in a moment). The amount of monetary reparations that Italy were levied was roughly $6,122,907,320.97 in today's currency, and this is not counting the loss of their overseas empire (in Europe, and Africa as well as concessions in Asia), in addition to having it's Easterly border being redrawn against her favor.

Additionally, Italy also faced levies on the size of their military and exactly where they could place defensive fortifications. The peace terms spelled out that Italy was to ensure steps were also taken to ensure that the Fascists were removed from the country and not allowed to return.

It is plain that Italy was to be held to blame as one of the 'lesser' powers in World War II.

##Cultural Blame

Now we get the second part of the answer which is, "Why Italy may or may not be held culturally responsible for World War II." Once again, we can go back to the Paris Peace Treaties for a clue to why this is, and it comes from the fact that the Allies and signatories accepted that Italy as a state was no longer a fascist belligerent:

Whereas in consequence of the victories of the Allied forces, and with the assistance of the democratic elements of the Italian people, the Fascist regime in Italy was overthrown on July 25, 1943, and Italy, having surrendered unconditionally, signed terms of Armistice on September 3 and 29 of the same year;

Secondly, the treaty also recognized that this State fought with the Allies towards the defeat of the 'big evil' Germany:

and Whereas after the said Armistice Italian armed forces, both of the Government and of the Resistance Movement, took an active part in the war against Germany, and Italy declared war on Germany as from October 13, 1943, and thereby became a co-belligerent against Germany

So from these treaties we are able to see that yes, it is possible to draw a narrative that Italy held a 'lesser blame' for the second World War than the first. I have previously spoken upon this subject in regards to how Italy avoided an occupation to the level of Germany and Japan but I want to expand on that to talk about the shaping of memory that Italy went on after the war to ensure that it was the Fascists that were seen as the belligerents, and not the Italian state and that Italy herself had suffered under fascism.

It is important to remember that the Italians were not treated well under Germany occupation after 1943. Italian soldiers which had surrendered to the Germans were deported back to Germany for forced labor, while the Italian units that resisted in any part were doomed under a confusing agreement reached between Germany and the Italian government. Episodes like the massacre at Cephalonia of 5,000 Italian soldiers were carried out under the orders of Hitler for an “exemplary punishment.”

The method employed by the Germans in the areas they controlled was simply and reductive: arrive in the morning, round up all the men, and shoot them. The bodies were then burned to destroy the evidence of German involvement. The Germans also attempted to frame these massacres (of which there were thousands over a two year period from 1943-1945) as retribution against partisan resistance. Women were raped en masse by the Germans in the area they occupied, and quickly put to death any resistance that were captured. There is some debate on if the Malaria epidemic in the Lazio region after 1943 that resulted from the Nazi's flooding of the Pontine Marshes was simply a tactic of warfare with the happy coincidence of leading to a malaria epidemic, or a deliberate attempt at biological warfare. The Salò regime was not one of collaboration as Vichy France was, it was without pause or equivocation an occupation. This occupation, and the grief suffered under it, continues to brew into the present as Italy consistently launches legal cases against the current German government for reparations onto its citizens.

The fact that it was the Italians themselves which had removed Mussolini and the Fascists before seeking rapprochement with the Allies in 1943 helped to view the crimes of the Fascist regime were in fact seen as just that, crimes of a regime that had been ousted and then actively rebelled against. The work of Benedetto Croce can not be underestimated at this point, as he would start the story that Italy had been just as much of a victim of the Fascists as other countries had.

With the outlawing of the Fascist party, Italy did undertake a period similar in scope to the German de-nazification while inspectors from the South accessed the remaining soldiers and bureaucracy to the North to understand what they did under the Salò regime (and thus if they were capable of continuing in service to the legitimate government). The British and the Americans, meanwhile, grateful for support during the Italian Campaign forwent any reparations during peace settlements and instead rewarded the ravaged country with billions in aid for the country to rebuild itself from the horrors that had been bestowed upon it during the war.

Elsewhere, monuments began to spring up all over Italy as this memory formed that they had resisted, which I talked about further here.

##Conclusion

Yes, it does seem ironic that the country which was the birthplace of fascism would escape much of the cultural blame in the public consciousness for the Second World War, the facts belie this. The very instruments that allowed Italy to re-emerge onto the world stage spelled out that Italy was to be blamed for the aggression of the war. Curiously, however, these same instruments also show why this sentiment that Italy was not held to blame have festered despite evidence.

The fact that Italy itself has also gone out of its way to emphasize the brutality that they faced during the war over their own role in bringing this aggression onto the world also explains much of this cultural memory.