Hey :!:
I have witnessed similar behaviour by Downy's in our backyard
during an attack/flyby from a Coopers Hawk.
The Downy will move/hide under a branch and freeze without moving until
the threat has moved on. Other birds use similar tactics and generally
"Hunker down" stay silent.
Mourning Doves aren't so lucky, they are the target of choice for Coopers "in my area".
I've watched a Coopers hawk enter the middle of a spruce tree
and come out the bottom with a puff of feathers and a
Dove.
napper