How? Especially if they've never learned the language/framework? This "Paul Bunyan" fairy tale of the "just do it!" hacker who can solve any problem no matter the odds just doesn't exist in real life.
Hello. I am this person. I am a generalist, I am not the best in any one area, but I have a broad range of skills across many domains. If I don't know how to solve a new problem, perhaps in a new domain, I will leverage the broad knowledge and learning skills to find out how to solve the problem. I won't be as fast as a specialist and there will be a greater risk of failure, but there is a good chance I will get the job done. I am not arrogant, I don't think I'm a genius, I don't think I am infallible. It's just that I am a generalist who likes to know a little about a lot, it's the way my brain works.
Learning just enough of a language or a framework to patch up a solution to a specific problem doesn't take very long. It takes a bit of experience, but it doesn't take a mythical hyper-productive hacker. The solution might not be pretty, and it probably won't scale to millions of users or stay solid for decades, but it will solve the problem. And in many cases, it's all that matters.
Even if you've never seen the language/framework, you dive in and learn it in an efficient and effective way, both from the current codebase and other resources.
Maybe you just haven't met the right people. I definitely "just do it" all the time. When I needed to develop a single page app for the first time, I just did it. When I found I needed to automate server deployments, I just did it. When a project I told someone I'd prototype needed me to design a circuit, fabricate a PCB, build it by hand and write firmware for its ARM microcontroller (including an OS), I just did it. And had fun doing it.
I'm sticking with my "full stack" claim. I think I've earned it.