I do understand your frustration but again to be pedantic, the type of software isn't conditional to how it's licensing will work.

I think there is a good discussion to be had over the licensing of LLM's and the fruits of training data, as well as that of the training data itself, but when it comes to the software itself, it's hard to argue what is and isn't open source.

> open source would mean that you can also download all the training data and re-do the training yourself

I don't think so.. Utilizing another data source, does not mean they're required, or even permitted in a lot of cases, to distribute that with their software/service.