I could not agree more. Programming isn't an employable d skill by itself. What you're actually doing for the business is problem solving, and in order to be good at that, you need to have people skills to a certain degree.
You listen to the managers, or are otherwise invested in the inner workings of the company. Using those skills of intuition, you gather the business objectives, and then write code to solve those needs in the manner most appropriate to the environment in which you work. Of course, often you're writing more than just code, and will contribute to documentation, and test with your users to gather feedback and improve your solution.
Good programmers spend less of their time writing actual code, and much more of their time understanding the problems their code is meant to solve.
Ultimately that's a job for the designers though. The coders job should be to just implement what they're told in a robust performant, but also pragmatic way.
You listen to the managers, or are otherwise invested in the inner workings of the company. Using those skills of intuition, you gather the business objectives, and then write code to solve those needs in the manner most appropriate to the environment in which you work. Of course, often you're writing more than just code, and will contribute to documentation, and test with your users to gather feedback and improve your solution.
Good programmers spend less of their time writing actual code, and much more of their time understanding the problems their code is meant to solve.