It is not true that reliability requires old-style engine design, it's more a question of cost. Modern jet airliners (their engines but also really everything about them) have a ton of complexity, including a myriad of electrical control systems, yet they are no less reliable.
It's just that this is not a fair comparison because manufacturers of said airliners have more resources for R&D.
Except now we’re back to one of the main points of the article - modern airliners cost billions of dollars to develop and certify, and GA aircraft will never get that level of investment.
Professional here also introducing an element that's unexpected. We expect that they'll have more training, they've often done simulator training which is more realistic, they have a lot more hours and so on.
But because it's a job they have much less Plan Continuation Bias aka "Get-there-itis". Flying New York to Dallas? I did that yesterday, and the day before, and the day before that. So if the weather looks bad and maybe we shouldn't, well then I guess we just don't go, I'll go tomorrow, or maybe somebody else will, it's just a job.
GA pilots are notorious for this problem, and it puts them in vulnerable situations where they're one problem away from disaster, as weather is worse than they hoped, things don't happen the way they expected, and gradually they go from "It'll probably be fine" to "I hope I live to learn from this experience".
It's just that this is not a fair comparison because manufacturers of said airliners have more resources for R&D.