First responders cannot formally declare anything, that's true, but if they think she is dead she won't get much help. Maybe she hit her head or maybe she has something blocking her breathing. She might just freeze to death because someone mistook her for dead and didn't wrap her in blankets.
That said, I am undergoing training as a first responder and we are instructed to not bother with checking the pulse, too many false readings, both positive and negative. We check breathing and whether they respond to voice, touch or pain (in that order).
If they don't have pulse, they are not breathing, and if they are not breathing you do CPR no matter if they have pulse or not.