Tertiary

I've finally been listening to the episode that includes a discussion of the word "tertiary." I think the problem is that the dictionary doesn't specify whether the noun modified should be a count noun (sorry; I don't know the correct term for that) or a collective noun. In other words, in the example given by the caller, was it a tertiary concern (a concern in the third grouping of concerns, as I think the speaker meant) or the tertiary concern, which is how the other person in the story seems to have read the definition. I don't think I've ever heard "tertiary" applied to a count noun, so that the modified word is a single item that's third in a list of single items.