Multiple blunders and mis-explanations such as "But on the Arduino Uno, we have a low drop-out voltage regulator. It dissipates less power in the form of heat". Now while the following sentences suggest that this allows the use of a lower input voltage, it is factually nonsense. And may not even be relevant to fake "UNO"s and clones - because people will often use these.
"The barrel connector needs a constant DC voltage supply in the range of 6-12V." Rather amusing, you may consider it acceptable but in fact, the whole purpose of the regulator is to permit a non-constant supply voltage!
"The Arduino Uno obviously cannot accept both inputs. Because without some management in place, that would lead to a surge in voltage." Called out in the comment section - this article appears to be quite recent - this is clearly foolish.
Worst of all, it completely misses what we have discussed here, the severe limitation of the on-board regulator which is really the most important point to understand. The article's focus on the cleverness of the supply switching mechanism - which really only exists to avoid the voltage drop of the diode used in the Nano - is basically irrelevant to deciding how to power the UNO so I feel the article really is not useful at all. 