Or is your definition of "open source" mean that a small indie dev should be able to reproduce the entire pipeline? Because that would disqualify more than just LLMs, but also hardware platforms like Arduino where you need to pay for manufacturing to get the underlying stuff built... is Arduino "open source?"
I much prefer the "open weights" term. It is not open source in the sense that you only get the finished product, not the actual source, but it is still open in the sense that it is not only accessible as a service.
For an analogy, take Quake for instance. When it was launched, its game server was available as an executable, so you could run it your machine, but that didn't make it open source. Only much later it was released as true open source software.