Before people get their backs up about the word "allegory" because of Tolkien's perceived dislike of it based on that particular quote, feel free to replace the world "allegory" with "applicability". I believe that Tolkien was simply making a semantic distinction in that quote, and there are many other instances of him admitting to the use of allegory.
In the Extended Edition of The Return of the King, at around the 34 minute mark, Theoden is informed by Gandalf that Pippin saw in the Palantir of Orthanc Sauron's plan to invade Gondor, and Gandalf tells him Rohan must prepare to send help. Theoden refuses, saying:
Tell me. Why should we ride to the aid of those who did not come to ours?
Of course, later on in the movie he has a change of heart, but in the movie at least (I haven't yet got round to reading the books), this initial refusal seems like a very significant moment.
Out of universe, we know that Tolkien was a product of the First World War and that it affected him significantly, so is there any material to indicate that Theoden's refusal was ever intended as an allegory for anything? What additional context, if any, do the books and Tolkien's letters add to this scene?