Onion and Garlic, a no-no?
Clearly, your flatmate was misinformed. Firstly, Italian cuisine is defined regionally. There are vast differences throughout the country, usually defined by local ingredients and historical influences.  However, there are many Italian dishes...from north to south that contain both onion and garlic.  It could be true that someone's specific recipe for, spinach, for example may only have onion...or only have garlic, but if you like the combination, there is no reason not to use it.  There is no such general "rule" in Italian cuisine.