What is the antecedent/modifier rule for it, them?

[niitorious]

Someone told me that in the case of ambiguity, it and them always refer to the nouns that are closest.

Is this correct?
What if there is no ambiguity in meaning, but these words are closer to nouns that do not match?

[JonathanSchneider]

This is a complex issue. The ultimate truth is that you cannot have a correct sentence that is also ambiguous. However, what makes a sentence ambiguous is tricky. In general, stay away from sentences where there are multiple possible antecedents for any pronoun. Thus, for a sentence with the word "it," dislike the sentence if there are multiple possible singular antecedents, etc.

As to how to identify the proper antecedent, this is a bit trickier. Yes, most often the antecedent is simply the nearest prior noun. However, there are cases where this is not true. In some cases, there is a slight preference for the subject or object of the original sentence to be the antecedent, so that ambiguity is minimized. I highly suggest that you familiarize yourself with the patterns shown in the correct answers of the OG to puzzle out this issue. While minimizing the cases where you have multiple singular or plural nouns before a singular or plural pronoun will get you most of the way there, true mastery of this issue requires more work than that.