contradictory info on appositives discovered

I got scared when I saw this document, which says (item 5) appositives are always nonrestrictive (i.e., giving unnecessary information). This is not what I taught in my comma lesson about appositives. In my lesson, I said appositives can convey either essential or non-essential information. So was I right?

While I'm not big on the Grammarly website, it does back me up:

Appositive nouns and noun phrases are often nonrestrictive; that is, they can be omitted from a sentence without obscuring the identity of the nouns they describe. Another word for nonrestrictive is nonessential. Always bookend a nonrestrictive, appositive noun or phrase with commas in the middle of a sentence. If the noun or phrase is placed at the end of a sentence, it should be preceded by a comma.

[...]

When an appositive noun or noun phrase contains an essential element without which a sentence’s meaning would materially alter, do not frame it with commas.

WRONG: My friend, Bill, owes me fifty dollars.

RIGHT: My friend Bill owes me fifty dollars.

There are no commas here because Bill is an essential description of my friend. We can assume from this sentence that the speaker has many friends, but the one who owes them money is Bill. The unlikely circumstance under which the first sentence could be construed as correct would be if the speaker has only one confirmed friend, and that friend’s name is Bill.

[T]hink of [a motorcycle with no sidecar]. This is the restrictive-appositive motorcycle. If anyone wants to hitch a ride..., they will have to ride double behind the driver. With this type of appositive, there is no disconnection between the driver and the passenger; they have their arms around each other. The restrictive-appositive motorcycle zooms out of sight—without commas.

So yes, restrictive appositives are a thing. In case you need confirmation from a more reliable source, here's CMOS, a.k.a. The Chicago Manual of Style. I can't link to the online CMOS because you have to be a subscriber, so I'm copying and pasting:

An appositive is a noun element that immediately follows another noun element in order to define or further identify it {George Washington, our first president, was born in Virginia [our first president is an appositive of the proper noun George Washington]}. An appositive is said to be “in apposition” with the word or phrase to which it refers. Commas frame an appositive unless it is restrictive {Robert Burns, the poet, wrote many songs about women named Mary [here, poet is a nonrestrictive appositive noun]} {the poet Robert Burns wrote many songs about women named Mary [Robert Burns restricts poet by precisely identifying which poet]}. A restrictive appositive cannot be removed from a sentence without obscuring the identity of the word or phrase that the appositive relates to. 

So again, CMOS confirms that restrictive appositives are a thing. I checked these references because I didn't think I was wrong on this point, but I did want to make sure. So the first document, linked above, is obviously wrong. Moral: always do your research.