Perhaps this is a case of the original concept of the test meaning one thing (all of the chords), but over the years, the testing has evolved into something else (as the proctors let things slip to just the one chord).
A military example, and one that even relates to the topic at hand:
In the US Army, the Bailey Bridge is a piece of equipment that we inherited from the British Army during World War II. It is a modular item, constructed of side frames, cross members, roadway components and various odds and ends, all of them painted battleship grey, and all having names given to them by the original owners.
Just why the thing is grey overall, alone in a sea of olive drab (when I was in, even the issue towels were olive drab), seems to have escaped the knowledge of anyone in the Army. I was always told that "it's always been that way" and that may be true. Inertia is a wonderful thing.
The one thing that got me the most about the Bailey (an item that I learned to hate during my brief stay in a combat engineer battalion post RVN) was that one component, the curb alongside of the roadway deck when the bridge was complete, was labeled the "riband". What the hell? Where did they come up with that?
(During all of the time that I inquired about this, sometimes with engineering officers up to the grade of colonel, none could tell me what a "riband" was. (And no, I never looked it up in the dictionary - those were not common books in your typical line battalion of any sort.) I first ran into the term when reading a book about transatlantic ocean liners, which coveted the mythical "Blue Riband", an honorary honor awarded to the ship with the fastest crossings of the ocean.)
The answer, of course, is that the British English term for "ribbon" is "riband", and that's the way it was shipped over to us. And, for almost seventy years, people in the US Army go around tossing off a bizarre word in place of a perfectly good American English one that would at least make some sense to the folks in our Army.
Now, the origin of the term was well lost in the mythical past when I first started ruffling feathers in my naturally inquisitive way. Yet, like the grey paint, the bridge component is still soldiering on, and will likely do so until we come up with a better way to erect semi-permanent bridges in a hurry. (Bailey bridging was used to temporarily repair one of the major routes into New Orleans following the hurricane and flooding - driving over those bridges brought back a lot of unpleasant memories of strained backs and amputated fingers.) And, I bet not one in ten thousand knows what the original makers of the thing meant when they named a prominent part a riband...
And, how does all of this relate? Well, another term for arpeggio is bridge...