Under investigation from TV licencing despite already having a licence

I did not bring a TV with me to Uni, but now that the law has changed about using iPlayer without a license, and owing to the need to desperately catch up on "Bake Off" and "The Apprentice," I had a license bought for me by my parents for the year. The other week, I received a letter from TV Licensing saying that I was "under formal investigation" for using iPlayer "without a licence. Judging it carries a maximum fine of £1000, this is quite a serious matter. The letter stated that I could "pay for a licence" or "tell us you don't need a licence," but mentioned nothing about what to do if you already have one, other than "ignore this and our systems will be updated soon." The closest explanation I can give to receiving this letter is that I hadn't registered my license online, but even that was such an arbitrary and non-permanent process that just looked like I was signing back in. I have no idea if I have "stopped the investigation," and until I do, which may be never, I am petrified to go anywhere near on-demand TV, which could make me miss entire series despite being able to watch them entirely legally. Have I "stopped the investigation"?