Accusations in Parseltongue are not true, the speaker merely believes them. (Actually, this raises the possibility of lying using a confundus charm. I'll assume that's banned by some Rule). If you were trying to mitigate the chance of someone destroying the world, you place a very high probability on them trying to trick you. The response is to use Hermione's algorithm that defeated LV earlier and place an ethical injunction on not killing Harry.

Now, that's probably a little harsh for the exam question, and LV won't necessarily adopt his enemy's tactic (even though it defeated him once and that's one of his rules), but I should think he requires substantial evidence to not kill Harry. More than an accusation of not being ambitious, which is explained by Harry's naivety.