"If you're pointing out your virtues to others, you have none to speak of."
Try that in an interview sometime.... If someones life is on the line, and you are more competent than the person or people trying to save them, then it would be not only bad, but possibly deadly, not to point out your virtues.
Yes, but there's a difference between "virtue", in the ethical sense, and "skill" or "knowledge".
I've actually been in the situation you describe. Yelling out, "I used to be a CPR instructor, she's a nurse, anyone better qualified? No? She's in charge!" may have helped save a life here by cutting through the "OMG whut happened?!?!" confusion of the moment. But that's different than "I am an exceptionally honest person, and she is very charitable!"