I'm not saying this is what happened, but I'm gonna throw this out there.
The medic was partnered with the patient's sister. As is most cases, partners become close friends, confidants, and have intimate knowledge of one another's lives. As far as adult relationships go, many partnerships come second only to the marriage. No doubt she knew exactly his skill set and what he could do. So, when his best friend and partner realised that he could and has performed the skills that could save her brother's life the distraught EMT begged and pleaded her best friend to do everything possible to try to save her brother. Being her best friend, he was incapable of separating his emotions from his professionalism.
I have no doubt that this was a highly charged emotional scene and mistakes get made when emotions are involved, Just think of what it's like when we transport pediatrics, This call would have been much more stressful.
Did he make a stupid mistake and a poor judgement call? Hell yeah, but if you haven't been on a call where you've had your emotions override your professionalism yet, it's just a matter of time.