But see, Claude can do nothing even better than it can choose between options. So why should that boss keep his job again?

"Bring me solutions, not problems" can mean "You are a competent, knowledgeable employee, who has identified a problem. You know enough to look at the alternatives and decide which is best, or at least which ones are workable. Bring me that, not just the problem."

And if it does mean that, it's empowering. You with your hands on the situation, you get to tell the boss what you think the best answer is, and the boss backstops you from deciding something that won't work in the bigger picture.