As the saying goes, a little knowledge is a dangerous thing. The writer of that piece of advice is badly informed.
To start, let's just look at these two versions of a possible sentence.
He is one of those men who is always on time.
He is one of those men who are always on time.
There are these two types of possible interpretation for the sentences:
A: He is one of those men. He is always on time.
B: He is one of those men. Those men are always on time.
Now it would be nice, wouldn't it, if sentence (1) always meant A, and sentence (2) always meant B. However, that's not the case. The fact is that native speakers, both in speech and writing, often use (1) to express B. The reason is that the word one often overrides normal verb agreement. In other words although sentence (2) definitely expresses B, sentence (1) would be used to express either A or B.
Here is what a vetted grammar source, based on real data, the Cambridge Grammar of the English Language has to say about this:
. . . The relativized element in these examples is object. Where it is the subject that is relativized, the expectation would be that the number of the verb would be determined by the antecedent, giving a plural verb in Type I, and a singular in Type II. In practice, however, singular verbs are often found as alternants of plurals in Type I:
i. He's [one of those people who always want to have the last word]. -- (Type I )
ii. He's [one of those people who always wants to have the last word]. -- (Type I )
iii. He's [one of her colleagues who is always ready to criticize her]. -- (Type II )
Examples [i] and [iii] follow the ordinary rules, but [ii] involves a singular override. It can presumably be attributed to the salience within the whole structure of one and to the influence of the Type II structure (it is in effect a blend between Types I and II ). But it cannot be regarded as a semantically motivated override: semantically the relative clause modifies people. This singular override is most common when the relative clause follows those or those + noun.
Now if you think about the following sentences carefully, you will see that the same thing applies:
- He is the only one of those men who is always on time.
- He is the only one of those men who are always on time.
C He is the one of those men. Only he is always on time.
D He is the only one of those men. They are always on time.
Sentence (3) could be used to mean either C or D. Sentence 4 can only be used for D.
In this kind of situation, thinking about the grammar is not the most useful guide. Even working out what the grammar is will take you quite some time. Go with your intuition!
The Cambridge Grammar of the English Language, Huddleston & Pullum [et al], 2002.