I've read so much conflicting info including statements like you can have a dry carbonated cider, a sweet flat cider, but not both unless you keg. I didn't understand what was magical about cider and yeast vs beer and yeast re bottling.
I think the opinions that you cite are stated with the assumption that we are only discussing the uses of "natural" sweeteners, such as table sugar, apple juice, honey, or the like. These are all simple sugars that are readily fermented to completion by the yeast.
In the keg, you can add simple sugars to sweeten, and keep it cold to slow the secondary fermentation, thus maintaining some of the added sweetness before it is converted to alcohol and CO2.
In the bottle, that can result in bottle bombs, because the sugars needed for sweetness are converted to alcohol and CO2. Bottling cider sweetened with "natural", simple sugars requires a pasteurization step to inactivate yeast once the desired carbonation level is achieved. See the Sticky post on pasteurization in this forum.
You're right in that there is nothing magical about cider yeast. The differences lie in the must (cider) and wort (beer). The wort contains unfermentable complex sugars that will add sweetness to finished beer, even when carbonated by adding simple sugar to the beer.
You notice the use of "natural" above. People think of xylitol as a "chemical", but it is found naturally in many fruits, in small quantities. The "chemical" label comes from the fact that the stuff you get in the store is produced via industrial chemical processes. This is generally accepted as your best option among the "artificial" sweeteners, and many people use it.