While it has been said so many times, "All is in Sanchin", the reality is that much of the practice in Uechi has evolved to a predominant emphasis on striking. Many don't incorporate ukemi, never mind sutemi, into the core program, despite the lament of Mr. Glasheen. Where we see these skills emphasized are in the dojo's that have an overlap in or concurrent curricula such as in your dojo, JoshW & JoeP, Bill's and, I assume, Raffi's.
To state the obvious, it's not unusual to fall in sparring and fighting. Ukemi is definitely needed to ensure you can do so safely and get back up. I think it is a gap in one's training to not cover that.
I think a point of clarification (for others, not you Mike) needs to made about ukemi and sutemi. Ukemi is the art of receiving a throwing technique and landing or rolling safely. Sutemi is the art of taking the fall -- either by necessity or choice -- and taking or throwing the opponent with the your momentum as you go down. Ukemi is the a necessary base for the development of sutemi.
Using the kotegaeshi example, when you flip over to avoid having the wrist broken, that's ukemi. When flipping over and grabbing the opponent's lapel/neck to take him over with you, that's sutemi.