You've asked a two part question.
[Is this a violation of] the international policy that a country should never refuse entry to verified citizens of their own?
In considering that question, the US example may be illuminative. The US requires US citizens to have a "passport book" when flying into the US, even though the US issues "passport cards" that serve as proof of nationality. If you can get to the border and prove your US nationality (by passport card or otherwise), they'll let you in, but airlines won't board you unless you have a passport book. If you don't have a passport book, you're supposed to get to the nearest consulate and apply for a passport before flying to the US.
But note that the US obligation to admit its own citizens is principally a feature of US law. CBP does not waive 8 USC 1185 because of some international body; there is no body that enforces international "policies" of this nature. Rather, they do so because they know that the federal courts would require them to admit US citizens based on the right of free movement implicit in US law.
If someone were unable to get into their country of citizenship and unable to gain legal residence elsewhere then unless they could remain on the run for the rest of their life they would eventually end up as the subject of negotiation between whatever country is trying to deport them and their country of citizenship. In other words, in the worst case, such people become a bilateral diplomatic matter between two countries. Therefore, any challenge to the restriction would have to go through the Italian or EU legal system.
Is this a violation of the EU freedom of movement directive, whereby a verified EU/EFTA national cannot normally be refused entry to any EU/EFTA state?
It certainly seems to be, but without a decision from an EU court, we can't be certain. From Article 5 of the freedom of movement directive (2004/38/EC):
Right of entry
1. Without prejudice to the provisions on travel documents applicable to national border controls, Member States shall grant Union citizens leave to enter their territory with a valid identity card or passport and shall grant family members who are not nationals of a Member State leave to enter their territory with a valid passport.
No entry visa or equivalent formality may be imposed on Union citizens.
This doesn't say anything about allowing EU citizens to board aircraft from non-EU destinations without their EU passports. So if Italy makes a rule that EU citizens need a passport to board a flight to Italy from outside the EU and Schengen area, that doesn't seem to violate Article 5 except by implication. It would be for a court to decide whether that implication is in fact present.
Because Article 5 doesn't say anything about where the passenger has flown from, we can also consider the case of a dual citizen of an EU member state and a "third country," who might fly to Italy using the third-country passport, and then present a national ID card at the immigration counter. If such a traveler were denied entry, that would appear to violate Article 5. If that traveler's other nationality were one that required a visa in the non-EU passport, the traveler might have a stronger case that Italy's rule infringes on the right of free movement.
EU or EFTA citizens could also challenge the restriction more generally as an infringement on the right of free movement that is established in the Treaty on European Union (TEU), even if the directive itself does not prohibit the restriction. For example, one might argue that free movement is restricted because there are countries to which EU citizens can travel with only an ID card, but from which they cannot return to Italy with only that card.
In addition, non-Italian EU or EFTA citizens could challenge the more restrictive regime applied to them on the argument that it violates the principle of non-discrimination articulated in Article 9 of the TEU:
In all its activities, the Union shall observe the principle of the equality of its citizens, who shall receive equal attention from its institutions, bodies, offices and agencies....
Furthermore, non-Italians residing in Italy could challenge the more restrictive regime on the basis of Article 24 of the directive:
1. Subject to such specific provisions as are expressly provided for in the Treaty and secondary law, all Union citizens residing on the basis of this Directive in the territory of the host Member State shall enjoy equal treatment with the nationals of that Member State within the scope of the Treaty. The benefit of this right shall be extended to family members who are not nationals of a Member State and who have the right of residence or permanent residence.