Radio service using battery I haven't used any type of radio services on my HTC one, not even Pandora or anything else because I just never listen to music outside of radio in my vehicle, but I have radio usage on my phone. What else could cause this service to be running?
Battery stats always lists consumers. If the mentioned entry would refer to "fm radio", it had listed the corresponding app as consumer.

You must be aware that the term "radio" is ambiguous here. It stands as an abbreviation for "radio waves", which in fact are used by "fm radio" – but also for communications using the cellular network. The latter is what you're seeing references as "radio" in the battery stats on some devices. Different devices might use different terms here, so a screenshot helps identifying the "item" by its associated symbol/icon, see e.g. What is Cell standby and how can I keep it from eating my battery?

With that link, I've also named how other devices might refer to this ("cell standby"). If your symbol looks similar to the one shown in the screenshot there, that would confirm what I've written here (note that it might look a little different on your device, not only due to a different manufacturer – but also due to the fact the screenshot on the linked question was taken with Android 2.3 ;)