Not really. I think you're assuming people are quite dim and can't react to the circumstances without very specific training. I went into break up a fight about a month back, got into contact with the opponent, slipped on the ice and took him down with me. I extricated myself from under him and got onto my knees and pinned him. I've never trained to do that, never even considered what I'd do in that situaton. I've certainly never trained on ice to have someone land on me while trying to take ukemi while trying to get a choke on. It was just the obvious thing to do with my training in the circumstances.
I was in a position which didn't suit me or what I'm trained to do, so I moved to one that did, that's a principle of Aikido; move to where you're strongest and work from there. I'd argue that for anyone with even a basic level of training in any art that is common sense.
I have been in similar situations (breaking up a fight and bouncing) and have had similar experiences and the results that you have had.
The fact that you could change the situation and dictate the terms of the fight means you were in control of the situation for whatever reason.
I think though, that you have to be careful with drawing the conclusion that it is not necessary to not train under the conditions that George outlines.
You were breaking up a fight. That could be much different than being the object of the fight. How much investment was the person fighting really putting into things to defeat you?
What happens when you can no longer dictate the terms and conditions of the situation? How do the environmental considerations impact you then?
Noise, smell, lights, movement....what happens when you are "behind" in the process and you are taking in lots of sensory information and trying to figure out what is going on?
This occurs when you are "ambushed" and trying to process all the input.
Sure, I agree, it is possible to NOT train as George states and be sucessful, apparently you were.
However, as you state, YOU decided to break up the fight. You were able to get into the fight and dictate the terms. Yes, I understand that you slipped on the ice and lost some of the terms, and it sounds like you were able to gain back control. I am sure your training helped you out in this area.
I'd caution against assuming that you'd be sucessful in every situation though. I think it depends on many things.
Things such as the level of investment of the person your fighting and his intent. THe number of folks involved, Light...space, etc.
One of the most dangerous things for someone, I believe is to actually have an encounter and realize success. It can cause you to discount and dismiss alot of other things and form a set of criteria that is totally framed around the situational conditions of that particular encounter.
Anyway, not trying to say you are wrong, as you clearly demonstrated that your training was good enough for that encounter.
I just caution you to make sure you understand the things in the situation that played in your success when you evaluate other situations based on your success!