I'm going to go with No here, but I'm not sure my No is really that relevant, because it gets caught up in the storytelling.
Details below, but first, I'm going to make my semi-annual pitch to stop using the term 'Inciting Incident'.
• When the term was invented (by Syd Field), it referred to an event on or about page 30. But since we have the idea of the Driver, I never know if people are referring to the First Driver or the Second Driver when they use 'Inciting Incident'.
• The Inciting Incident, according to Field, is when things go wrong. It's all good, and then it goes bad. Again, we know this isn't the case (Vader shows up really early). Why perpetuate a term that isn't very good?
• It refers to an incident, which implies an Action Driver. Again, this is limiting.
• It refers to a storytelling moment, not a storyforming moment. That's why it's always on page ~30.
So, anyway, back to my No, the First Driver is not motivated by the OS Problem Element, Issue, Concern or Domain."
In Lord of the Flies the First Driver is pre-book and is the crash of the boy's plane into the island. This is neither not definable by Work or Induction or even Situation. What it does is set up a story for those things to be important.
In 12 Angry Men, you certainly set up a playground where Production and Mind become important, but actually going off to the jury room is none of these things.
I think it feels like these things are all connected because in good stories, things feel connected. It's easy to look at Lord of the Flies and say, "Oh, the first driver puts them on an island, so it's motivated by Situation." But that's focusing on the The Story and not the Driver. I also think these things line up because of economy. It's a faster way into the story to make everything connected -- if you wanted to tell a romantic story about people meeting in Hawaii, it's wise to introduce Hawaii and the Romance together, but you could easily have a guy get to Hawaii, get fired from his job, go to a bar to get a drink and meet a gal there.