So I couldn't help my curiosity and went ahead and bought me a Strontium Nitro On-The-Go USB (16GB). I've never used a OTG device before so I've been itching to try it out. A OTG USB key suits me just fine. I can download stuff not usable on my HTC One when a PC isn't on hand, transfer it to the USB key then simply plug it into a PC later. Perfect.
Now I just need to actually do that.
So, yes, the HTC One has OTG capability but that's nothing too interesting. You'd expect a flagship to have that although it wasn't trumpeted in the spec sheet. Simply plug in the USB key and you'll get a notification saying the HTC One is in USB Host mode and can't charge the battery while it's the host device.
So how does it work?
You can create a new album in the Gallery app and specify the album be stored in USB storage. That will create a folder by the same name in the USB OTG device. Just copy any picture or video into the album if you want to use USB storage instead of phone storage.
Music in the USB key will appear in the Music app but there doesn't seem to be a way to manage songs in USB storage directly within the app.
Any decent file manager app should be able to access the files inside. I used ES File Explorer which didn't have problems with it. Using a File Manager app should also render any lack of file transfer capability in other apps irrelevant. Simply transfer them using the file manager. Still, it's much more convenient if you could just do it from the relevant app.
The USB key does get mighty hot after a while though but only time will tell if this negatively affects the USB key in any way.