First, it seems like a marketing photo-op for the CEO. In your opinion, is the author trying to make Rockefeller relatable? You can see how it works with HN readers.
These days his success is attributed to business acumen and notorious practices, not engineering, but I haven't read much about him. What impression does the book give?
Also, I would argue that the time he spent on solder drops was a waste of company resources much more valuable than solder: his time. What would he say if he saw the machine operator similarly wasting company time or resources? Rockefeller would have helped his company much more by improving his own efficiency.
Finally, in most companies when Rockefeller asks if you can reduce the number solder drops and you are the lowly solder machine operator, you reduce the solder drops no matter what. There is no way that story could have ended differently, and nobody would reveal that the boss's idea had bad consequences: The barrels had to be handled more carefully, they leaked at a higher rate, they had to increase some other sealing process to compensate, etc.
All my cynicism may be unfair, however.
EDIT: A bunch of edits