It's modeled after mission burritos. You could say it's San Franciscan. That's essentially Mexican.
Going from first principles is a different story. Did you know potatoes come from Peru, South America? Shouldn't they be called Peruvian Fries? Not French? Like half of all food is South American. It's wild. Same for beans; which make up a part of a Chipotle.
Anyway, when dealing with cultural categories there's no real facts to rely on. See sandwich vs hot dog.
I'd say it's Mexican, but not sit-down-Mexican. That's something different. You usually get wet burritos at sit down Mexican. There's a million places call like El Rodeo, or La Michoana, or whatever. They aren't a chain, but you know what you're gonna get at a sit down Mexican. It's never a Chipotle style burrito.