I think the process of data acquisition isn't so clear-cut. Take CERN as an example: they release loads of data from various experiments under the CC0 license [1]. This isn't just a few small datasets for classroom use; we're talking big-league data, like the entire first run data from LHCb [2].
On their portal, they don't just dump the data and leave you to it. They've got guides on analysis and the necessary tools (mostly open source stuff like ROOT [3] and even VMs). This means anyone can dive in. You could potentially discover something new or build on existing experiment analyses. This setup, with open data and tools, ticks the boxes for reproducibility. But does it mean people need to recreate the data themselves?
Ideally, yeah, but realistically, while you could theoretically rebuild the LHC (since most technical details are public), it would take an army of skilled people, billions of dollars, and years to do it.
This contrasts with open source models, where you can retrain models using data to get the weights. But getting hold of the data and the cost to reproduce the weights is usually prohibitive. I get that CERN's approach might seem to counter this, but remember, they're not releasing raw data (which is mostly noise), but a more refined version. Try downloading several petabytes of raw data if not; good luck with that. But for training something like a LLM, you might need the whole dataset, which in many cases have its own problems with copyrights…etc.
[1] https://opendata.cern.ch/docs/terms-of-use
[2] https://opendata.cern.ch/docs/lhcb-releases-entire-run1-data...
[3] https://root.cern/