The long tradition refers to the use of tooling in general, and could mean that, since past tools were accepted, recent tools like LLMs can be fair game as well.
But, since there can be doubts about this interpretation, them saying explicitly if LLMs are permitted or not could be beneficial. But then again, maybe they don't want to commit to an hard rule and have more freedom to decide on a case by case basis, or just don't advertise that LLMs are welcome to prevent a flood of vibe-coded submissions.
In both cases you cannot get permission.