Learn English – What does “not one of them“ mean

^†This is where logic or mathematics operates differently from human language (aka natural language). Strictly speaking and mathematically speaking,

1. "N is Y, if not Z" would be read as
2. "if N is not Z, then N is Y".

However, in many human languages, English included, saying 1 doesn't mean just 2. To understand this, we should think a little about the motive of a speaker who said 1.
Quite likely, the speaker's intention was

3. "If N is not so great as Z (or any quantity > Y), it is = Y"^‡.

But to say 3 exactly in those words would be clumsy,
and thus the speaker would naturally rephrase 3 as:

4. "N = Y if N ≠ Z",
or in plain English: 5. "N is Y, if not Z".

We can try another approach to show that if not can be used to mean perhaps even.

Let N is the number of people who has an attribute Q.
Consider these two following propositions:

(a) N is Y, if not Z.^†
(b) N is Y, perhaps even Z.

Let N_a is the set of all possible values of N for proposition (a).
It is easy to see that N_a = {Y, Y+1, Y+2, Y+3, ..., Z}.

Let N_b is the set of all possible values of N for proposition (b).
It is also easy to see that N_b = {Y, Y+1, Y+2, Y+3, ..., Z}.

Now, it is clear that N_a and N_b are equal. Hence, (a) and (b) are equivalent.
Thus, if not can be used to mean perhaps even.
Q.E.D.

The phrase no one of them is "grammatical" (taking that to mean that it is both idiomatic and meaningful), but it is not always the same thing as none of them. It is an emphatic form employed to distinguish a proposition concerning a number of entities taken singly from propositions concerning the same entities taken in combination.

Consider the difference between these two propositions concerning three people, Adolphus, Benjamin and Carloman, suspected of murdering Dionysius.

1. None of them killed him. This is taken to assert that all three are innocent of the murder.

2. No one of them killed him. This implies the possibility that two of them—A and B, or A and C, or B and C—or all three, conspired to commit the murder.

So it might be perfectly proper to say of three utterances that "No one of them is grammatical" if you intend to propose that some combination of the utterances is grammatical.