A general rule against Italian passports is of course wrong and illegal.
But if an airline suspects a passport of being fake then shouldn't they be within their rights to ask for further ID?
I believe it's possible to be airside in CPH without going through a Schengen or other EU border (although I think one would have to go through security) so the passenger having passed through Danish passport control is neither here nor there.
However I hope the passenger gets satisfactory resolution and that other Italians are no longer hassled in such a manner.
A general bias against Italian passports is also wrong and of doubtful legality.
It's possible to be airside in CPH without going through a Schengen or other EU border, but the passenger having passed or having to pass Danish passport control is of relevance. Danish border control at CPH has facial-recognition-technology in use for at least some of us there and do use it in conjunction with the passports routinely enough.
I'll have to check with my contacts in the Danish law enforcement/security services, but I would be surprised if they confirm that Italian passports are the majority of encountered fraudulent ID around CPH. There are bigger fish in the sea to fry.