No, it isn't. The radio station (commercial ones at least) pay on the basis of their Net Broadcasting Revenue -
clicky.
As I don't work in the radio industry I have to assume that this is the profit/income the station receives by broadcasting. In the case of a commercial broadcaster the bulk of that is presumably from advertising revenue which in turn is based on the number of listeners the station has.
I find it somewhat difficult to believe that the listening figures for the BBC and commercial stations are calculated based on the idea that everyone out there listening is doing so while on their own or at home with their family. The idea is patently ridiculous. There must surely be some sort of accommodation in the figures that takes account of people who listen to the radio while at their place of work.
This is why I think the PRS are taking the p!ss. They get paid by the radio companies based effectively on the number of listeners they have and this must take into account people who listen at work. They then want any premises apart from private homes to pay them again for the privilege of listening to something that the PRS has already been paid for once already.
As an aside, should you have to pay the PRS to listen to the radio in your own garden for example? Or in a semi detached or terraced house? Or with a window open? Other people may be able to hear the broadcast if you do so.
I do accept your argument if we're talking about people listening to CDs at work. Like publicly available films they are sold specifically for personal use and there are specific prohibitions against their use for public broadcast so playing them at work counts as a breach of their terms of use. But there is a massive difference in the mode of delivery between a CD and a radio broadcast.