After making this comment, can you confirm why you think the problem is always the dogs fault?Similar cope that some come out with in this thread... yet another confused owner who thinks they're good and their dog is harmless etc.
The owner made all the mistakes here;
no lead on the dog
no ability to physically control the dog
refused to even get involved with the event
Again if bought up correctly with boundaries and authority, the dog should not attack other parties human or animal.
As for your same incident of the staffie, even though you'll turn round and say, "oh but you are only one", I have had my own and seen a number of staffies around horses without a problem. So it is not all dogs or the breed is naturally violent or wanting a tear up with other animals.
Secondly and most importantly, again this shows extreme owner negligence - Dog was off the lead, could not be controlled, owner was many meters away shouting at a dog who does not have boundaries or authority installed in it. A third party got off their bike and restrained the dog as the owner could not.
Again, please tell me straight why this is the dogs fault and not the owners.