Absolutely untrue. CPR is recommended by the AHA for anyone who isn't breathing, regardless of whether they have a pulse [0].
By "she may have had a weak pulse", I mean that she may have had a weak pulse that wasn't felt. That's not asystole technically, but it results in the same treatment.
Emergency situations are, understandably, high-adrenaline scenarios and mistakes get made. Even professionals aren't great at detecting carotid pulses properly all the time [1].
> In both of those cases, the patient will have no pulse
Absolutely untrue as well. Only VF is pulseless. VT can present both ways [2].
0: http://circ.ahajournals.org/content/122/18_suppl_3/S640
1: http://www.emsworld.com/article/10320480/the-vital-signs-par...