In case of synchronic negligence, Adam at the time of acting has evidence that should bring him to realize that he's endangering Bob, but simply fails to appreciate this risk. I'm inclined to think that Adam is blameworthy for his action in this case (to some degree). So at least synchronic culpable ignorance fails to fully exculpate. He really - i.e. in the strictest sense - should have known better. We owe it to each other to be more careful than that.
Holly Smith, in 'Culpable Ignorance' [pdf], seems to dismiss these as poor test cases of whether ignorance always exculpates. The closest she comes to explaining why is when she writes, "if the agent's act is not justified relative to his actual beliefs, and he realizes this fact, then of course he is to blame for performing the act, but we cannot infer that any blameworthiness arises from his culpable ignorance." (p.545)
This is a puzzling remark. For one thing, talk of blameworthiness "arising" from culpable ignorance risks changing the subject -- a point I'll return to shortly. What's more immediately relevant is that the section I underlined unnecessarily confounds the issue -- it's true that if he realizes his act is unjustified, then it's not really a case of full "ignorance", and so a bad test case. So cut that section. What if the agent doesn't realize his act isn't justified (even given his actual beliefs or background knowledge) -- wouldn't that, at least, be a legitimate test case for whether culpable ignorance exculpates?
Consider Smith's example of a driver who fails to check his rear-view mirror before backing out of his driveway, and so crashes into an oncoming vehicle. Smith claims (pp.545-6):
The driver's ignorance is undoubtedly culpable, and it leads to his performing the wrong act, since if he had checked he would have seen the car and avoided the collision. But we cannot infer from this that his culpable ignorance makes him blameworthy for colliding with the car. For the driver is blameworthy quite independently of his culpability in failing to check his mirror: his background knowledge that the street often has traffic on it makes his decision to take the risk of backing up quite unjustified.
This seems to change the subject, since the original question was whether culpable ignorance excuses us from blame, not whether it's what makes us blameworthy. The relevant structure is this: the driver does something bad (namely crash into an oncoming car); the driver didn't realize that his action would have this bad consequence; but the driver is still blameworthy for the outcome because his ignorance was culpable rather than reasonable. That is, he should have realized (given his background knowledge) that his action was unacceptably risky, even if in fact he did not realize this.
[It's true that we cannot infer from this that "culpable ignorance makes him blameworthy", if anyone were to care about that question, but we sure can infer that culpable ignorance does not (fully) excuse him from blame for the crash -- which was, I thought, the question under consideration.]
Why does Smith switch questions like this? She argues for her approach as follows (p.545):
The fact that a single act can be culpable on more than one count means that we can decisively settle the question of whether or not culpable ignorance excuses only if we focus exclusively on cases in which the agent's culpable ignorance is the only possible source of blameworthiness.
But this just seems confused. If we are considering whether culpable ignorance excuses, presumably we are considering whether it excuses some other wrong act -- killing someone, say -- which is the presumed source of blameworthiness. It's an additional, very different (and seemingly analytic)* question whether culpable ignorance is itself a source of blameworthiness.
* (Aside: perhaps it's not really analytic, e.g. if we're asking whether epistemically culpable ignorance is also morally culpable, or some such. Though the 'diachronic' cases arguably invoke morally culpable negligence right from the start, so there it seems that Smith must be concerned with some yet further question -- e.g. the question of moral luck, applied to negligence cases, which I previously argued was an entirely independent question.)
Now, I take it that what really follows from the possibility of normative overdetermination is that "we can decisively settle the question of whether or not culpable ignorance excuses" only if we focus exclusively on cases in which the agent is culpably ignorant of all the decisive reasons against his action. This suffices to avoid the problem cases wherein the agent is partially ignorant, but knows he should investigate further before acting, and hence "knows himself to be performing an act less good than its alternative, namely conducting further enquiry." (p.546) There the agent might be blameworthy for the failure to investigate, rather than the unwitting killing, and so we would attribute blameworthiness to the agent even if their ignorance excused the latter. A fair test must avoid such merely partial ignorance, then.
But this condition is easy enough to meet, and we're still left with many possible synchronic cases of the sort that Smith too-hastily dismissed. Again, just take the example of the driver who should know to check his rearview mirrors before reversing, but one rushed day it simply doesn't cross his mind that he has any reason to do so. Here, we stipulate, there are no confounding wrong-making features that he remains aware of. So it's a genuine test of whether (culpable/irrational) ignorance exculpates. And, intuitively, the answer seems clear: the agent is still blameworthy for his unwittingly reckless behaviour (even though he would, of course, be even more blameworthy if he had knowingly endangered others' lives).
Perhaps Smith is simply interested in a different question, which is fine, so long as we're clear about what the discussion is meant to establish. The paper presents itself as addressing the question whether culpable ignorance exculpates. If that's the aim, then it seems to me to end up wide of the mark.