Check out consumer reports if you are buying a new appliance. Your local public library likely has a subscription.
I bought my current fridge about 6 years ago for very little ($150? $100? I can't even remember) from a guy on Craigslist who had it in his garage. He did not offer me an extended warranty, but he did load it in my minivan. I also bought a used clothes washer and dryer from neighbors that year. Again, I was just gambling my money away I guess. Since then I have bought a new dishwasher and a new clothes dryer using the Consumer Reports method. No extended warranty, no problems with either.
I can't even be bothered trying to make someone honor a warranty on something as piddly as an appliance. More hassle than it is worth. MMM shares this life philosophy:
http://www.mrmoneymustache.com/2017/04/25/there-are-no-guarantees/
Sorry, but this makes little sense. Appliances are becoming less reliable as they are built in third world countries, to rigid price points, and are loaded with electronics. It's nothing to have a fairly new major appliance in need of a $400-600 repair, within the original warranty period, typically because it needs a new control board, touch screen, or ECU, and two service calls, to address the problem. If you "can't even be bothered trying to make someone honor a warranty on something as piddly as an appliance" you certainly have a different viewpoint that most folks who are careful shepherds of their hard earned money.
As for how this apply to the MMM article you link, it's simple, it has nothing to do with what he is conveying. As a homebuilder, I dealt with lots of appliance issues, frequently as a service to a customer who would find it incredibly inconvenient to deal with problems with their new vacation home, hours from where they are conducting their day to day life. One of the reasons I did it was because it was about as far from "trying to make somebody honor" a contract as it gets. A five mine phone call with the manufacturer's or sellers 800# including an appointment made with a local, factory authorized tech. and your done. Be there to open the door for the guy, and get hundreds of dollars of repairs done with no money exchanged, no hassles, no drama. For something as unreliable and poorly built as a typical
digital dishwasher, fridge, range etc.... a low cost, or free (via credit card ) extended warranty is well worth it.