It ain’t only corporations, it’s casual, intuitive, everyday speakers—the community that owns the language—arriving there naturally from the regular meaning of individual words: They see a work that appears to be created by some form of intelligence/creativity. No natural intelligence created it. Hence, a work of artificial intelligence.
See? Not that hard. No need to be difficult about it. Nitpicking a casual speaker over it is bound to earn you well-deserved disdain.
Right: that’s the right order.
Do web searches care about word order, though?