> My understanding is that there's somewhat of a gray area for requests that do not accurately enough specify the information desired. The agency in question can basically say "We don't understand what you're requesting, so there is no information."

This is essentially correct. Under 5 U.S.C § 552(a)(3)(a)(i), the request for records must reasonably describe such records. In addition, the 9th circuit has declared that "reasonable description relates not only to subject matter, but also relates to place of search..."