> The OSI's take on this is that an open source model can be modified through fine-tuning etc, even if you can't rebuild it from scratch.

By this definition almost any binary can be "open source" since hex editors exist. (Or more usefully, you can use ghidra et al. to do more interesting changes.) I know GPL has a very specific view of things, but I'd like to quote an excerpt that I think is generally applicable from https://www.gnu.org/licenses/gpl-3.0.html -

> The “source code” for a work means the preferred form of the work for making modifications to it. “Object code” means any non-source form of a work.

Which is why I'm fine with "open weights", because that's saying the object code is under an open license.

> The problem with requiring "build from scratch" for open source models is that the number of interesting models with training data that can be openly licensed is close to zero.

So? If the number of open source models is zero, then the number of open source models is zero.