Should the title be corrected to source-available?
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...
Though, I do think it's still acceptable if you just point how to get the data (i.e. if it was the offline version of Wikipedia and then URL to that) if actually providing the source data is overwhelming. Offering to provide a copy at cost would be quite acceptable (i.e. I deliver the media to you to make a copy).
But if there's no way another person can acquire that data, even in theory, then I think it's pretty clear the source was not open. Just use the more appropriate term and everyone is on the level what the release is about.