I couldn't disagree with you more. That isn't problem solving. That's management.
What you describe is a manager's view of problem solving. They basically don't want problems in the first place. It is a manger's role to ensure succession planning, training, resourcing and appropriation documentation and standards are maintained. A manager doesn't have to do them all. Just create the environment through appropriate "stick & carrot" measures.
Problem solving is a rare gift. I know many competent Design Engineers that cannot solve problems. Most good ones can follow patterns and apply them to new situations. They're the ones you want to do most day to day designs. They'll need attention to detail. But again, they'll get stuck at something that doesn't fit within the those patterns.
The true problem solver is one that can make those intuitive leaps. They can see patterns, where others don't. Or even work with a thousand disconnected clues to get to the root cause. The very best do have a formal background (and they'll draw on those bits of lectures and notes when needed, going back to 1st Principals). Unfortunately, this is difficult and mostly can't be put down in Manuals and Procedures. This doesn't necessarily make them appropriate for Design and quite often they are terrible at mundane tasks. So bad managers don't know how to value or deal with this skill.
