I know what you are saying at the same time doing CPR on someone who has merely fainted is a great way to kill them because you didn't bother to see if they were still breathing.
Here's the thing -- except perhaps for doctors, everybody else in the medical world follows protocols that someone else has already established. First aiders, EMT's, even nurses don't sit around thinking about the theoretical aspects of a situation. They are trained to follow protocols, a pre-determined decision tree leading to specific actions under specific conditions.
The current protocol for first aiders is NOT to check for pulse. You do check for respiration, in fact, you should be checking for an airway obstruction before doing anything else. Having established that you are not dealing with an airway problem then if there's no respiration, and the person is unconscious, you start CPR.
The old protocols used to say check for a pulse, but that has been removed from the updated protocols. The reason why is that there are very few cases where there is no airway obstruction, someone has a pulse, but is not breathing. Those cases are rare compared to the number of people who die while a first aider tries to find a pulse in a high stress situation under non-ideal conditions. Was that a pulse? Or a twich? Or was it just me being nervous? People die on the ground while the first aider is trying to figure it out, who could have been saved if they immediately start CPR.
So the modern protocols say go directly to CPR after finding that the casualty is not breathing and has no detectable airway obstruction.
P.S. - MrsC's responses are a bit suspicious in that they were all written from a theoretical perspective whereas anyone with medical training would write from a protocol / established practice perspective, for something as well studied as CPR and cardiac issues in general.