Sure, but the article is talking about a completely different meaning of reproducibility, where a researcher uses an LLM as a tool to study some research question, and someone else comes along and wants to check whether the claims hold up.
This doesn't in any way require the training run or the build to be reproducible. It just requires the model, once released through the API, to remain available for a reasonable length of time (and not have the rug pulled with 3 days' notice).