Learn English – Can a colon join sentence fragments for emphasis

This may be more of an extended comment than an answer, but the cited rule (if I understand it properly) seems illogical. Sentences can end in verbs. So, if colons can come after complete sentences, then colons can come directly after verbs.

For instance, here’s a sentence from this week’s Economist:

Lviv displays formidable discipline and self-organisation in its self-policing: taxi drivers use their radios to report anything suspicious.

If we replace in its self-policing with in how it self-polices, then we have a verb directly followed by a colon:

Lviv displays formidable discipline and self-organisation in how it self-polices: taxi drivers use their radios to report anything suspicious.

Here's another example of one of their sentences and a paraphrase that ends up with a verb + colon:

But the two sides should not overdo it: they need each other.

But the two sides should not exaggerate: they need each other.

Maybe the rule needs rephrasing—or abandoning.

To build on the point that @BladorthinTheGrey is making, grammar describes the way words are related to form meaning in sentences. But there are other ways to form relationship that express meaning, including page layout devices such as labels or headings, or parallel constructions such as tables.

A word (or a few words) followed by a colon is a common way of attaching a label to a piece of information. This is one of those non-grammatical uses referred to in other answers, and it is non grammatical because it is outside the scope of grammar. (That is, not concerned with the construction of sentences.)

So, Examples: is a label in the example given. It is a common and accepted way to create labels, but it is outside the scope of grammar because it is not part of a sentence construction.