My mum's husband is a painter and decorator. Every house is different, but he has built up a set of skills over the years he's been active that allow him to broadly apply his knowledge to understand how to solve a problem.
Similarly, I can't always solve the problem, but I do know where to start asking questions, and I do know how to follow those up efficiently. Is this when I Google for the docs, for answers to a problem, for a place to find help? And then after that, it's about knowing the next steps, knowing which part is likely to be the next relevant thing to Google/research.
Do I get stuff done? Sure. Do I remember how to do it next time? Sometimes. But sometimes it's just enough to know how to start solving the next problem. I think we just feel a bit fraudulent because Google is easier. I'd be surprised if anyone ever said "Am I good at xxxxx or just good at going to the library, choosing the right books and reading the required parts?"