In many government jobs, the criteria for moving a task forward is the ability to check off a tick box. So you do not admit you do not know the answer; you give a plausible answer that lets the officer check the box. That's the case for most govt questions. Very little depth is required in the answers as not everything can be validated in the timespan of an interview. So admit you know what a binary tree is and talk about it in high level terms. Unless the officer was a previous programmer, the checkbox gets checked.
When you say you do not know or answer a different question, it makes it harder to check that box off. Most officials just want to check a box and move you (and themselves) on. Don't make it difficult for them.
You assume that the box says next to it "can answer questions about his career specialism correctly". It probably doesn't. More likely it says "does not appear nervous when asked about his career specialism, and appears to know topics he claims to know" or something more like that.