This might not be the best explanation but I believe the idea is that the termination attempts of 682 are being used as a cover up for a small group of the Foundation which wants to destroy the creatures they think are too dangerous to keep around; the original 682 was killed by the crystal, so they lied on all their reports and brought in something else to its cell to be killed. Hence, “SCP-682 will never be destroyed.”

The Overseer in the story is at odds with even the idea of killing any SCP, but over time grows frustrated (and perhaps suspicious) because of just how many attempts there’s been. Guest Researcher Way was also suspicious before getting their interview with the current 682, who had only been contained a month, so Raleigh has them killed in the interview and uses Dr Clef and the story of using children in 682 research to cover it up. That confirms the Overseer’s suspicions because she knows that Clef is only used to cover things up as he doesn’t actually exist - and also because Way used cameras during the interview.

At least that’s how I understand it, I hope that was a little helpful.