I reckon the PRNG seeding in such a case might be used during development/testing.

So, run the code with a seed in a non distributed way (e.g. in R turn off all parallelism), and then the results should be the same in every run.

Then once this test output is validated, depending on the nature of the model, it can be run in parallel, and guarantees of deterministic behaviour will go, but that's ok.

I didn't develop the model, so can't really say anything in depth beyond the published materials.

I just found it odd at the time how this specific detail was incorrectly used by some to claim the model was broken/irredeemably buggy.

Edit: Actually, in general, perhaps there's one other situation where the seed might be useful, assuming you have used a seed in the first place. Depending on the distributed environment, there's no guarantee that the processes or random number draws will be run in the same order. But it might be that in most cases they're in the same order. This might bias the distribution of the samples you take. So you might want to change the seed on every run to protect yourself from such nasty phantom effects.