Don't get me wrong.. I'm not saying that the Italian system/maturita is a joke - although the way the high school system is headed it will soon become one. My point is that Bocconi takes on just about anyone - I have a countless number of friends studying there who just about managed to pass their maturita - now if that accounts for 50% of the admission process, as you say, the only way they could have gotten in is by doing brilliantly in the test - this, although possible, is highly unlikely.
For "foreign" students there are no specific requirements - all you have to do is send your "dossier" and well you are quite likely to get in. Now, I admire their attempt to attract international students - probably the only university in Italy to run courses in English - but the filtering process for such students is objectively poor.
Oh and Tremonti may not be an exceptional minister (though Italy has lacked an exceptional minster for the economy for a very long time - I'm gradually convincing myself that the phrase "Italian economy" is incompatible with the attribute "exceptional") but he is proably one of the most accomplished accountants in Italy - one of the big magic circle firm - can't remember which, probably clifford chance - has established a partnership with tremonti's firm.
Don't get me wrong - until very recently I thought that Bocconi was the haven of Italian higher education, then when I experienced it first hand.. huh...it left me utterly disappointed. However, it is irrefutable that it remains one of the best choices in Italy - probably along the other two other private institutions: Cattolica and LUISS - but given the grave underfunding of public universities in italy (and here they complain!! In italy they are lucky if they get any funding for research at all and here the big four whine about the fact that 150m a year is not sufficient - hence the inevitable "brain drain" that is so talked about in italian papers) it is not at all difficult for private entities to stand out.