Lots of people have access to natural language AI — Google search, voice assistants, WolframAlpha, AI dungeon, GPT-J — so if you agree that Coke doesn’t get to say they’re “democratising” soda because that’s a misuse of terminology, you should also agree that commercial deployment of a natural language AI API doesn’t get to say they’re “democratising” AI because that’s also a misuse of terminology.
(I mean, like coke, they could say it, but it wouldn’t make sense.)
Possibly one could claim something is democratizing access to some specific aspect?
I do think it probably best to tend away from using the term unless it is a particularly good fit though. (“Best” as in “what I would prefer”, not as in “most profitable”)