I understand the analogy to other types of critical data often not included in open-source distros (e.g Quake III's source is GPL but its resources like textures are not, as mentioned in the article). The distinction is in these cases the data does not clarify anything about the functioning of the engine, nor does its absence obscure anything. So by my earlier smell test it makes sense to say Quake III is open source.
But open-sourcing a transformer ANN without the training data tells us almost nothing about the internal functioning of the software. The exact same source code might be a medical diagnosis machine, or a simple translator. It does not pass my smell test to say this counts as "open source." It makes more sense to say that ANNs are data-as-code programming paradigms, glued together by a bit of Python. An analogy would be if id released its build scripts and announced Quake III was open-source, but claimed the .cpp and .h files were proprietary data. The batch scripts tell you a lot of useful info - maybe even that Q3 has a client-server architecture - but they don't tell you that the game is an FPS, let alone the tricks and foibles in its renderer.