[Eomer of the Rohirrim]

A most interesting question that I had never considered before. We know that the Black Riders were in the village because of the numerous references to terror, which only they possess. But as to who broke into the inn? Maybe the Riders told Ferny et al to go and fetch the Ring and bring it back to them. This would explain why the intruders did not sense that the Ring was in a nearby room.

But would the Riders trust the Men? And, if I remember correctly, the Riders at all costs wanted to avoid being seen. I think they feared the prospect of having a roused village standing up to them in challenge. So I think that once the first room proved to be a red herring, the Riders fled, not wanting to disturb the peace anymore.