I want to share a look at this from a bit different perspective.

As a kid, I would fix, trade and sell older radios and TV's for money and other things. I fell in love with vacuum tube era things. They are beautiful and it's all human scale. You can see the parts. Back then, I didn't have much. Our family was in poverty a lot of the time. Reasons. That's not a big deal, and in fact, was of great benefit to me personally. It kind of forced exploring the world and meaning to get something out of it. I needed it!

Anyway, I had a couple of old ratty texts from the 50's era that explained the theory of operation. And I had various toys and projects that showed parts of that theory to me. A crystal radio, for example. I must have reread that text 50 times.

At first, I understood very little. Being young, much of the higher level stuff would blow right by. But the general concepts were there.

So, imagine being faced with the radio. You don't have much, no fancy test gear, etc...

I submit Feynman didn't fix the radio. It's still broken in a sense. But, what he did do was make that radio, imperfect or broken, damaged, as it was, perform as needed. He moved the problem out of the way.

This is important. The radio is a system. It's designed to do a task, and it's parts are designed to perform to a specification or other. Each radio is kind of unique too. Whatever flaws it has gets compensated for.

Problem: Noise in the radio audio

Think real hard:

Here, one can start to analyze the radio, take the theory of operation and identify where noise might be coming from. This means one has sufficient understanding to solve the problem in the first place. The heavy lift is realizing it!

But, say one does not possess that level of understanding. I didn't back then. Not until many years later, lots of fixes under my belt, and some kind souls giving me test gear.

So then, as a system, what's still possible? Fixing the radio may not be an option due to lack of components, understanding, tools.

Move the radio
Swap the tubes
Modify antenna
Change power source
Change adjustable things in the radio
Remove something from the radio
Etc...

For each of these things one CAN do, which of them may resolve noise?

In this way, the problem shifts from, "fixing it", which implies the radio is brought from a flawed state to an acceptable one. (just less and more minor flaws really)

That is what Feynman did. A poor component at one stage of the radio may perform another task just fine. Swapping the tubes does that.

For many years, I would get this gear from people. And it was a lot of, "look at the problem", "think real hard", "execute solution."

And a bunch of that boiled down to what I could do, not so much what should be done, or needed to be done. And a lot of that was successful. Try stuff, observe, try more stuff, observe. After a time, which stuff to try boiled down to a potent set of things. More successes.

I would get an older TV, for example. Maybe it had a red tint, or the picture bloomed. One could make adjustments in the set to re-balance the picture, or improve focus, limit overall brightness, and any number of things to bring that particular system into a functioning order sufficient to perform the task required of it. Still broken, in the technical sense. New components would very likely improve it, but a removal of one, or replacement with similar one, even removing one, tweaks to the unit, all could combine to make it perform.

In my following of Feynman, I find a consistent theme where he was very good at understanding basic understanding. The calculus book he refers to contained some general solutions he found could solve a very broad set of problems. Rather than explore all the solution sets and struggle to apply them, he would take a very useful one and max it out, applying it everywhere. Where it would not work, or was impractical, he would seek another one.

I see this as a very important aspect of this awesome problem solving ability he demonstrated. Collecting things like this, as well as taking problems from various angles:

What can be done, and could it help?
What has been done before?
What should be done.
Combine things done before.
Guess at possible new things to be done.
etc...

seems to be major contributors to this skill.

Feynman often mentioned puzzles. When you combine a "gauntlet" of puzzles and Feynman's natural ability to recognize fundamental understanding with time and a zeal to solve, his remarks about "not being a genius" have some real merit!

Now, he was, and that's not really a matter of serious debate. But, the method, to him, is more about doing the work to be lucid. Solve, solve, solve, refine tools, collect new ones, solve, solve, solve...

The difference here, between Feynman, and us ordinary mortals, is the breadth and depth of that lucidity.

Those skills I learned in my early youth still apply today. I can't tell you how many times I've arrived at simple ways to "fix" something, just based on what could be done, and inferences on what must be true. It's theory of operation, coupled with broad experience and that "gauntlet" of puzzles run with "the tools"

Each of us can do this. Some of us can do it extremely well in a given domain too.

I feel Feynman never did appreciate his skill and lucidity about reality itself, the world, it's parts. Few of us have that.

But, the Feynman way of looking at things, solving problems, collecting tools to solve them with, being observant, and inference:

What is possible?
What can we do?
What must be true?
Etc...

Is something everyone can cultivate to varying degrees, depending on our affinity for a given domain, personal attributes, and resources.

I know this is a zen like argument, but he didn't actually fix that radio. He made a broken one, or flawed one perform better.

And in that last bit is an important realization:

We state the problem. Fine. But, we need to also state the goal too.

Given a goal, the problem may be too limiting. A solution may appear out of reach, or not be seen due to a problem statement constraining things, or masking things.

Work backward from the goal and sometimes one can factor the original problem statement away. And in the doing of that, arrive at a solution that gets it done, or renders the problem a non problem.

And I'll add Feynman did the work. A lot of it, and he credits that to a lot of his insights. Solving a bazillion puzzles will turn anyone into a much better solution finder, and he's right about that.

Do the work. Seek the puzzles, and keep at them. Over time, one gets an internal sort of understanding that is more broadly applicable.