I will answer your last question:
What are (if there are any) the requirements for a diet to be defined
Quality of existing diets is expressed by the so-called "index values" which are calculated by checking if a given diet conform to a special set of guidelines (hopefully, scientifically validated). Different countries have different guildelines and therefore different indexes, eg. in USA there is the Healthy Eating Index and in the Netherlands there is the Dutch Healthy Diet index. I do not know what is being used in Italy. Now, all these diets may have their strengths and weaknesses but their overall index-score can be high which could lead to labelling such diet as "healthy" despite some deficiencies.
Now, for example, in this article (it's in Polish, sorry, but this is only for example, you can try to find other articles in English or Italian using Google) three diets for children are compared: vegetarian, vegan and traditional. The Healthy Eating Index is used as a measure and the scores are: vegetarian 57,7 points; vegan 90,2 points; traditional 24,9 points. The Vegan diet seems to be clearly superior in comparison with the traditional one.
Now, I do not say that I agree with this method and its results, but I think that this is possible reason for someone to call vegan diet as "proven healthy".
If you want to further pursue this subject, I would recommend to read more about those different indexes.