It would be plainly illegal for Italy to insist on there being 3 months of validity in passport for an EU passport holder. As a matter of EU Law, you would be entitled to enter Italy even if you were trying to enter on the last day of passport validity.

What is more, even after that, it would be illegal for them to deny entry as long as you can establish that you are an EU national by any means and I would have thought that even a recently expired EU passport would be good enough for that purpose.

This sounds to me like something left over from pre-EU days.