And don't get me started on Sesame!

I think it is fitting because they provide „all“ models independent from the provider. Open in this sense means to me being open to switch the model, speed and provider at any time.

I used to demand the same but a word can have multiple meanings depending on the context, eg OpenMind means something specific. Open{$IT-term} does not necessarily mean Open Source {$IT-term} and OpenAI might mean an AI available to all people, not implying anything about cost. What could be illegal is the word Free, which a for-profit company would never use in the first place.