This seems like an odd use of language to me -- the pronoun refers back to a particular thing, not a particular word, and the thing that's needed for clarity and definiteness is that there should be one thing, not one word.
Consider:
"The puzzle contained one red herring; it led a few solvers to waste some time." (Antecedent is "red herring"; a red herring is not actually a herring and it doesn't make much sense to say that what the pronoun refers back to is "herring".)
"The puzzle contained three red herrings, of which the last but one was particularly liable to confuse; it caught out many solvers." (Antecedent is "the last but one [of the three red herrings]"; if you had to pick out a single word it would have to be either "herrings", which is plural, or "last", which is Just Plain Wrong.)
"Mary went through the list of candidates to find the most suitable for the job. She sent him an email containing a job offer." (Antecedent is "the most suitable for the job". No single word will do.)
I'm guessing that "one-word antecedent" is US educational jargon. I don't like it.
A couple of more drastic examples to ram home the point that pronouns refer to things (or maybe ideas of things) rather than to words as such.
You and I walk into the office and I point at one of the people sitting at a computer. "He's one of our best engineers. You should give him a pay rise." (The antecedent is merely gestured at, not mentioned in words at all.)
I come into the room where you're listening to Bach's "Well-Tempered Clavier", and say "He's so good at fugues." (The antecedent is merely implied by context. No words, no gestures, nothing.)
Consider:
"The puzzle contained one red herring; it led a few solvers to waste some time." (Antecedent is "red herring"; a red herring is not actually a herring and it doesn't make much sense to say that what the pronoun refers back to is "herring".)
"The puzzle contained three red herrings, of which the last but one was particularly liable to confuse; it caught out many solvers." (Antecedent is "the last but one [of the three red herrings]"; if you had to pick out a single word it would have to be either "herrings", which is plural, or "last", which is Just Plain Wrong.)
"Mary went through the list of candidates to find the most suitable for the job. She sent him an email containing a job offer." (Antecedent is "the most suitable for the job". No single word will do.)
I'm guessing that "one-word antecedent" is US educational jargon. I don't like it.