Every example of a NN I've seen is good at one thing, the thing it is trained for. I haven't yet seen a NN that can beat people at chess, recognize faces, drive, and make coffee, or more importantly, decide when to do one or the other. The closest thing I can think of is Watson from IBM.
People can drive (poorly) but they also recognize the value of life in a biker or a squirrel, and in some cases, override their usual learned behavior, for example, instead of continuing to drive, swerving, basically improvising.
Computers and programs again are good for what they have been input and now, what they already have learned. The synthesis part, I'm not quite sure even NN have reached that part yet. I may be wrong, the answer is probably "learn more" or "learn faster" (which is what you suggest), but it's easier to synthesize like this when you have a mind with general knowledge, at which point the mind is less like a NN and more and more like a person.