Indeed, and even for software it’s not a solved problem. Open Source is not an impediment of reproducible builds, but it’s not its main objective.
I didn’t take the word “reproducibility” in its scientific meaning, because there is scientific debate of whether that’s even possible to achieve.
As you noticed, the authors have made concessions about the role of modern compilers so their text needs to be read knowing that they’re experts of European copyright speaking to EU regulators (it’s a policy brief).
I suspect the authors used the word “reproducibility” to make a general point (just like they did with the equivalence source/object code). I’m reading it as what the OSI FAQ calls the “right to fork”: give third parties the abilities (tools) and rights (legal terms) to learn how an AI has been built and build a similar one without having to start from scratch.