In HC it doesn't matter if the cheat death mechanic is slightly unreliable. If it procs, you were dead anyway. Any chance, even a tiny one, of reversing that is worth having.
And UA procs first because it works differently to Firebirds.
Firebird's res's you after you've died, but UA prevents a fatal damage attack. When you see it that way, obviously they can't proc at the same time, and UA will always proc first.
And may the odds be ever in your favour.