it's this and it's also the observation that burn in (with no on/of cycles) leads to a longer lasting, better working unit... especially as it relates to capacitors.
Explain to me how that works with with capacitors. I have more than one EE degree, including actually finishing undergrad at MIT, and the only changes I have heard involving caps are when electrolytics are "formed", but that happens pretty much instantaneously if you turn on the unit and supply full rated input voltage to it. It doesn't take 100 hours, and you don't do it by just turning on 120VAC (Or 240VAC). I guess this also applies to Tantalum caps, but nobody should ever use those since they provide little benefit compared to other types and tend to catch fire when they fail. Electrolytics also have incredibly poor tolerances and shot not be used in any location where a precision value matters. If your design's performance changes greatly because of the exact value of an electrolytic, you done screwed up.
Component part and product level failure rate is described as having a bathtub shape. You have a high rate initially from parts that may have been improperly made or handled, or products that were assembled incorrectly, and after a long time you have cumulative stress related failures at an increasing rate. Maybe somebody forgot to add the thermal compound to a part before installing a heatsink. Maybe they dropped a part on the floor or handled the board without proper static protection. This is why products are burned in. For amps you cycle power output levels from low to high to heat and cool the parts and bring out thermal cycling faults. Some products I've designed (for semiconductor processing) were placed in chambers while running at full power and heated and cooled while vibrations were applied. This would bring out part failures, but also assembly mistakes like forgetting a lock washer or not siliconing the electrolytics in the supply correctly. We did this to catch early life failures and improve the reliability of the shipped products. But nobody from any level of the company (marketing, engineering, test, reliability, manufacturing, executive) ever once said "this is definitely going to make this work better." There is a reason that all tests confirming performance is within spec are done before the burn-in tests.
My guess is that people saw that burn-in testing was done at some companies, asked about the practice and completely misunderstood what was explained to them. And then the lore was passed around.