Open source does not require full working implementations. There's no requirement that a code snippet that I release be fully working and identical to a complete solution.
About the access of binaries or providing working implementations, where did those come from? I don't think this thread was discussing those at all.
Indeed I would be willing to call something an "open source model" if it came without weights, but did come with the training data and with a documented process (preferably executable); and a release with just the training data could be called "open dataset" while the software to run the training would be just plain old open source software.
And, of course, a model with only the model data distributed with an open license is relatively commonly called "open weights", this being pretty self-explanatory term.
You already have access to all the training data everyone else is using.... You can download an offline version of Wikipedia. Here's every Reddit comment for a decade: https://academictorrents.com/details/ba051999301b109eab37d16...