These two assertions ('shooting was an accident...' and 'she was within her rights...') are not inherently contradictory, though. That's what's remarkable about Kettle Logic: genuine contradictions can be employed in a proof in a convincing (and not necessarily invalid) manner. The above can be orthogonal or complementary assertions, but they are not contradictory.
That's not kettle logic, that's a mode of legal argumentation that deals with boolean "and" constructions of a law.
If some charge requires both [A] and [B] for the accused to be guilty, then this argument is that it's neither [A] nor [B], but the defendant is innocent if they can prove either half of the argument, since the condition is "[A] and [B]", not "[A] or [B]".
Whether they were within their rights would only come into play if they had the requisite mental state (intent, recklessness, etc., as for the crime charged) in the first place.
> That means that in some cases you have to argue that you killed someone intentionally to avoid being convicted
No, you don't.
It's just if you are charged with an offense that requires intent, the question of self-defense (or any other excuse) is moot if the prosecutor can't prove intent beyond a reasonable doubt in the first place.
If you are charged with an offense that doesn't require intent, like involuntary manslaughter, you don't have to argue intent to kill to use self-defense as an excuse.
And even of you are charged with an intent crime, you don't need to grant intent to argue self-defense.