It absolutely doesn't. It sounds like further diluting the term "open-source" isn't great.

I assume when people say "open source model" they mean "open weights model". The "open source" term doesn't really make sense here, since machine learning models are not compilations of source code. (Though DeepSeek has published several papers with details on their training process. It's more than just open weights.)

ML models do have a "source" though

If ML models have a source, brains have a source.

Brains don't have a source.

Therefore, ML models don't have a source.