This has nothing to do with logic, and everything to do with the hybrid status of Latinate Germanic languages. Your author is trying to remove a real problem of English semantics which is contextual, with a context-free rule. Such things seldom work, and the same flaw can be pressed into other quantifications, but it is much less common.
The same single problem he is trying to avoid here infects all modal verbs, including 'is', in this kind of construction. It is always ambiguous whether a modal verb's referent, or the modal verb's sense, is complemented by a following 'not'.
(Wittgenstein in "The Blue Book" raises this as a way of indicating how deeply contextual even the most basic grammatical aspects of a language can be. Labeling the two options 'non' and 'ne', he points out some complex problems of the meaning of negation we solve constantly without realizing there ever was an ambiguity.)
Two clearer examples:
"He may not leave." can mean that he might stay or that he must stay.
"He could not finish the course." can mean that he is still in the course and might drop out, or that has dropped out already because he cannot finish it.
The meaning is totally dependent on its context.
And for your case:
"All dogs are not black" can mean that a randomly selected dog might not be black or that a randomly selected dog will not be black.
The problem is with the whole class of verbs, and not with the quantifier.
But the rigidity of the other quantifiers makes the ambiguity irrelevant.
"Some dogs are not black" could theoretically mean there are dogs that might not be black or there are dogs that are non-black. But logically these have the same result: We cannot count on all dogs being black. It does not matter whether we know there are actual exceptions, or we only do not know whether-or-not there are exceptions.
"No dogs are not black" (besides just sounding stupid) could theoretically mean that there are no dogs that are not necessarily black or that there are no dogs that are non-black. Again, the more definite pronouncement swallows the less definite one logically, because the impossibility of a non-black dog rules out the impossibility of a possibly non-black dog, and vice-versus.
"All dogs are not black" does not resolve this for us. The idea of dogs in general being actually non-black, is not related in the same way to that of dogs in general being possibly non-black. The one gets us only non-black dogs, the other just some non-black dogs. These two ideas are much more independent.
In this way, all is the 'weakest' or 'most open' quantifier, which is what leads to its use as the default quantifier in open constructions. So of the common quantifiers, only 'all' really shows the weakness of the construction inside it very often.
Since it does so, however, you should take your author's advice and work around using it in any canonical form.
Beyond that, it pays off, in general, to incorporate negation into an adjectival form (non-A) or resolve it with deMorgan's laws or exclusive constructions (relying on unless, except, only, etc. for clarification) and then pull the negations back out of their embeddings at the time a representation is formulated, after any processing of the language has taken place.