I read it as being related to the "line in the sand" idiom. There exists some set of rules, the "line". Exactly what is and isn't allowed under those rules is a bit arbitrary, like the exact location where you would draw a line in the sand with your finger. What matters is that the line has been drawn, and everybody knows that the line may not be crossed.

Under that metaphor, a person may stay very far from the line, to avoid accidentally stepping over it, or they may walk right up to the line. Metaphorically, the former would be a person who refuses to answer any questions about nuclear secrets, regardless of whether the question can be legally answered. The latter would be a person who knows exactly what can be legally answered, and will give as full of an answer as is allowed. They know where the line in the sand is, and have walked up to the line.

It means going to the limit of what is allowed, the line represents some limit/law/threshold that cannot be crossed. In this case the veil of secrecy that separates what is/is not public about nuclear weapons.

Normally you would stay well away from said "line". Occasionally though someone may "walk" right up to the "line" but no further.

You can take it to mean that someone knows something secret but is carefully only talking about what isn't secret. The risk is that they might inadvertently reveal some information of what is beyond the line.

To "cross the line" means that you went too far, in this context meaning that someone revealed secrets or otherwise talked about things that they shouldn't reveal. So to walk up to the line means that the person was willing to talk about the topic or share their knowledge, but did so without "crossing the line."

It’s related to the term crossed the line, which I believe originated with Cesar crossing the rubicon. Crossing the line means breaking some rule or taboo in a way that has significant or permanent consequences. Walking up to the line is getting close without crossing.

ChatGPT's really good for that kind of a thing, but in this case it's a saying popularized by a Johnny Cash song about staying loyal and committed to his wife while being on the road and facing temptation.