Look at what happened a while back at that UCF tailgate party...I can recall a couple of tragic situations in DC when "old clothes" Officers responded to crimes in progress and were accidentally shot by Uniformed Officers. As a result, "tactical units" as they were called then, were limited to responding ONLY to Signal 13 (Officer in trouble) calls and to leave "in progress" responses to Uniformed units. Even as an Investigator, wearing suitcoat and tie, we were very careful to be recognized by Uniforms before showing our weapons and avoided unneccesary responses to situations where we were far enough away to be pretty sure marked units would be on the scene before we could make it.
The problem in cities with large depts. is particularly acute when responders are from precincts or districts OUTSIDE the place of the incident. usually local cops recognize one another but may never have seen an officer from another unit.
Yep, interjecting yourself is very dangerous but, sometimes, the right thing to do as in the OP's scenario.
I have actually had civilians accost me while effecting an arrest on a BG who they thought was a victim. We did look like thugs, though.
The plain clothes UCF officer got shot by the uniformed county officer that was responding, (If I got the story right) I guess they weren't aware that there were undercover guys there in the crowd... all they knew was that there was a guy wielding a gun!!!Everyone was doing their job but it turned out tragic......for all involved..I am sure it won't happen again...