Were you really focused then? Not having distractions but still staring blankly at a screen, is not the same as focusing.
Worst case, even if you try 100 things and none of those works, you know that these 100 things are not the solutions to the problem -- something that you didn't before. And you didn't just reject 100 random things, but 100 things that you legitimately could consider as solutions.
I've never not had at least partial results when I have been focused. I've had nothing too many times when I was distracted.
More, I've had plenty of brief diversions into a topic that produced more learning than some deliberate attempts I have made.
I think the "true Scotsman fallacy" is often used as a way to dismiss actual classification mistakes.
What one calls focused might not actually be focused -- humans are easy to deceive themselves.
Besides, I don't see what other possibility would there be. That being focused is not important? That people can just as well achieve the same (or even more) things when unfocused vs when focused? That we need special statistical studies to be able to tell that working focused on that work is better? None of these look plausible to me.
If what you're saying is that sometimes non-deliberate attempts can work too, that might be so, but by definition those are non-deliberate, happy accidents.
You can't program these. What you can program is actual work -- and that better be focused, than, "I'll fool around for weeks with other things until inspiration strikes".
So, why then don't we encourage more practices that encourage happy accidents?
I accept that the one argument is more appealing to emotional logic. I am highly suspicious of arguments that speak to that form of plausibility.
Then I'm arguing that you're an outlier in that.
And I'll add that for most people, even those happy accidents come when they're engaged in focused work -- not when they're having distractions all the time. Do you really get happy accidents while some colleague annoys you with questions every few minutes, or while checking your Twitter and Facebook and not doing anything specific?
(Twitter and Facebook? Yeah, not so much.)
Do, could I be an outlier? Certainly possible. But I don't think it is a safe thought. More likely, I am a near average person. Which is why I would love studies actually demonstrating this.
I would certainly be interested in more/followup studies regarding this matter.
Appeal to the times I've been focused for a time gets me to ignore all of the times I did the same and produced nothing. Not only produced nothing, but consumed nothing, as well. Both have happened. I do not keep a solid journal to say that one happens more than the other. One certainly made me happy, so I can remember it better. But that is the definition of selection bias.