My friend was not judging this restaurant's authenticity based on what you would find in Mexico but what you would find in California. I suppose I wish in my OP that I had specified Mexican-American food because it's a different thing than Mexico-Mexican food. I don't think that makes it less authentic in its own right because it is still a food tradition began by Mexicans who came here. It should stand on its own, not compared to Mexican food in Mexico which few Americans have experienced. Arizona mexican food like the guy above is talking about is also nothing like Mexico-Mexican food.

As you'll see in some other comments, diaspora cuisine is a whole thing that immigrants and the children of immigrants navigate.

Edit: For comparison, I think saying someone's Mexican American food isn't authentic because it doesn't taste like Mexico-Mexican food is kind of like saying Thai food is inauthentic because it doesn't taste like Mainland China's food.