So a program built with an non-determinisitc compiler cannot be open source? Or even just a C program that will change based on the order each object file is built? What about build time stamps?
You can absolutely open source an LLM, it's just that noone has. And you can absouletely bundle the random seem with the training data, it's just that, again, noone has.
And runtime randomness is hardly an issue. We write programs with RNG in them all the time and noone takes issue with that