For some reason, it seems taboo to say "I don't know how to do that". Even if I add "but I'm really good at figuring things out quickly", it doesn't seem to have much of an impact. All the person heard was "don't know how".

I would MUCH rather hire someone who is a quick learner and can adapt and figure things out (which in my opinion, is the sign of true intelligence -- "problem solving") rather than someone who is knowledgable in a niche area. Granted, there are exceptions, and if someone is designing a nuclear reactor, you can bet you want someone who is an expert at that one thing. But generally speaking, I think polymath abilities are much more useful.