The quote would be clearer if it spoke of the difference between the reading in which all boys didn’t run and (that in which) some did.
In the positive version “every boy ran”, there is no ambiguity: 100% of the boys ran.
Logically, “every boy didn’t run” follows the same pattern: for each boy x, the statement asserts that x didn’t run. That is, the negation in “didn’t” applies to the action “run”.
The problem is that in English, the form has also been used idiomatically to assert something different: that not all of the boys ran. That is, the negation in didn’t applies to the qualifier “every”.
Here is a classical example:
- all that glitters is not gold
Wikipedia traces this (or variants) to a Latin quote dated to the 12th century or earlier, and popularised by Shakespeare in The Merchant of Venice.
The article mentions a 1175 version by the French monk Alain de Lille: "Do not hold everything gold that shines like gold", where the logical meaning matches the literary intent. The version popularised by Shakespeare, however, sounds more catchy even though its logic is wonky.
As a result, the literary meaning of the form “all that (...) is/does not (...)” no longer matches its literal/logical meaning.
One might try to argue that the literary meaning should be deemed ‘incorrect’ or ‘inaccurate’, but it is precisely this kind of idiomatic usage of language that lies behind the ambiguity your quote highlights.