thats the idea, FM radio piped in to the box. You don't need a rebroadcast license any more than if you were playing it over a loudspeaker. Before I was ever a tech I remember calling local businesses and having a radios station be the on hold music. Most stations are fine with this. More coverage. More exposure. Back in my hometown the local cable provider played one of the local radio stations over the information channel. Don't think there was ever an FCC issue. Plus I have a background in broadcasting... The only way a licensing issue could come up would be if the company was making money directly from it. Once the station pumps the signal over free radio waves- what happens, happens. Not much can be done to stop it.
This is actually more common than some people think. a lot of phone systems have a feature for it.