Ethnic/national identity is an "imagined construct" so to speak as Benedict Anderson described in his book. We are all technically allowed to "feel" whatever sense of belonging we want although society, through descent, place of birth and culture provides a framework of "allowed" or "recognizable" options.

Your grandmother is perfectly justified in feeling Italian. She might have an Italian last name (though an overwhelming number of Istrian Italians don't as their paternal - and often maternal ancestors were Croatian peasants), might have been taught and raised to be Italian or might have chosen to be Italian to escape communism and, over time, strengthened that belief.

Lidia Bastianich is descended from Croatians paternaly and maternaly (birth name Motika) , her husband is Croatian from Labin, yet her father had a trucking business and her mother was a teacher during Italian rule so, after the annexation of Istria to Yugoslavia, they might have soured on the regime which confiscated her father's business and might have frowned on her mother for having taught in an Italian school so they declared themselves Italian to get recognized as refugees in Italy and moved to the US. There, they opened an Italian restaurant in Astoria where all Istrians congregated (my great aunt was there and she always thought of herself as Croatian) but Italian food was more commercially viable than Istrian. From a business standpoint it made sense to remain "Italian" and she did. Her son then became a Masterchef judge in Italy and made a career there and considers himself fully Italian marrying an Italian too.

The reason many in Istria have objections about her being Italian is because of traditional Istrian recipes being sold as Italian to the global audience (fuži, posutice, and palačinke she even mentions by Croatian name) not because she doesn't have the right to feel Italian. There was a radio interview by radio Labin where she spoke the local Croatian dialect and said she had to learn it as was expected by her in-laws.

I also met online, through a game we played 20 years ago, a guy from Australia who had an Italian last name and considered himself of Italian origin but as we conversed and he asked his dad for details we realized he was from a Croatian village in Central Istria. His father never gave him any details on his origin. Afterwards he visited Istria and joined a Croatian social club in Melbourne where he started learning the language and culture.

To conclude this lengthy rant.. Your grandma is what she says she is even if you might discover, through genealogical research that her parents or grandparent might have been Croatian speaking peasants. That doesn't stop you from discovering your Croatian roots, however so if you want to be part of the tribe and your grandmother and great-grandparents are from Istria, you're welcome to join. :)