Weights are not binary. A model is created at init time, with random values. After that, it is being modified using data. The key point is that the labs modify the models "as weights". That means that weights are the intended / preferred way of modifying a model. Which, coincidentally, matches the definition of source in Apache 2.0. There is no "higher level" place where editing takes place. It all happens in weight space. Through the license you get the same rights as the lab that created it: view, inspect, run, modify, re-release. That's it. That's the only thing a license can grant you.
The rest is semantics, misunderstandings, and FUD. A model released under an open source license is open source. Training data is lab knowhow / IP. Which, historically, has never been required for any open source release.
Well, you can't add or alter data in pre-training from just the weights. Which, as I understand it, means you can't fundamentally increase core knowledge or cognitive ability, only what the model likes to do with those. You can only post-train, and you're subject as a result to catastrophic forgetting.
To explain simply as far as I can tell (would love to be corrected) the large number of pre-training tokens only works because the documents are randomly ordered.
So if you e.g. took a foundation model with open weights, then tried post-training it all the new data since its cut-off period, it would then end up over-trained on that new data, and forget older things.