On the only time I have fallen, Bow was able to stop almost immediately.  I 
was "out" for a couple of minutes.  He not only didn't, he wouldn't allow 
anyone except my husband to touch me.  (Never heard of a "guard" horse...)
He refused to leave even tho my friend's mare was in prime time heat.  He's 
a really special horse!
The only time Bow ever misbehaved at all...  I had always ridden western on 
him.  I put an English (hunt seat) saddle on him and when I put weight in 
the stirrup, he acted like someone stuck with a hot stick!  A friend 
suggested that the problem was the saddle was a bit narrow but I just went 
back to using the western saddle!  (I used it for competitive trail rides on 
him also.)
Best wishes,
Vickie