The military will certainly step in and discipline the individuals. The location of the incident will also be a factor in the determination of who takes care of it. On base it certainly will be, off base it may or may not be handled that way. The country is also important. In the US and many places where bases are, the authorities will turn over people to the MPs.
Getting injured in a fight is not an accident; it is a lapse of discipline for soldiers to get into fights (other than fighting the designated enemy, of course). Falling off a ladder is an accident because you didn't intend to fall off the ladder. Getting into a fight is something you do intentionally, and if someone breaks your wrist, they did that intentionally too.
Every Day Carry.....such as the equipment that police officer carry everyday or everyday offduty...basically there normal carry package of equipment
faults commited against a law enforcement officer is taken very seriously in a court of law. This does not mean they will allways win. So you might make your case in court but I highly do not recomend you go with the freedom of speech in mind causing offduty police officers to waste their precious off duty time on you. Note that the prosecution success rate for lude speech towards a law enforcement officer in the year 2008 was .02%