Well.. If it was good for Rihanna and and other "behind the scenes" documentaries... I think it is good for amateur film makers as well...
You seem to have made a number of inaccurate assumptions based on one photograph and then publicly posted those assumptions as fact:
1. As I said; for a quick and dirty, opportune interview by a journalist, I'm sure some of them use a H4N.
2. With an actual BBC filming crew (rather than just some journalist), the PSM would NEVER use just a H4N! Think about it for a minute, the BBC is one of the most respected TV networks in the world with a multi-billion dollar annual turnover, do you really think their film crews would be using hand-held prosumer quality audio recorders?
3. I very much doubt Rihanna reviewed the audio recording made by the journalist and therefore would have no idea whatsoever whether or not it was "good".
4. If the audio recording from the H4N was in fact used (which is unlikely), it would have been cleaned/processed by extremely well equipped, highly experienced audio post professionals for it to even stand a chance of passing BBC QC. And even then, it's entirely possible that a special dispensation had to be negotiated by the producers to enable the audio to clear QC.
5. Lastly, and given the points above, it is in fact only in exceptional circumstances and therefore very rare that a BBC TV production would use just a H4N to record primary audio, even for just a short segment. "Very rare" is pretty much the opposite of "a LOT", which is what you stated as fact.
Given a half decent external mic on a boom and someone with a half decent idea of how to use it, it's entirely possibly for an amateur filmmaker to achieve usable (by amateur standards) production sound using a H4N as the recorder. Without an external mic however, the sound quality using just a H4N is generally going to be just marginally better than using a camera's built in mics. If your filmmaking goal is to achieve marginally better quality than the average home video then yes, a H4N or a H4N attached to a boom pole would probably be good enough. However, I suspect most IT members joined IT, at least in part, to learn how to achieve substantially better than average home video standards.
G