The badge said PA, but he told ED employees he was a student there. When we have students, their badges often say the level of training they are pursuing (e.g., "RN" or "EMT-B") but have the school's name on them and they are wearing a different uniform (e.g., white scrubs for RN students instead of blue for RNs).
As for CPR, I agree it'd be a bigger deal if the cardiac pt had not been resuscitated due to this kid's CPR; however, it is noteworthy that a person w/o a pulse is already clinically dead. Even if performed correctly, the chance of a return of spontaneous circulation and ultimate survival is extraordinarily low. (In the case of a hospital setting where the pt was seen to code, the chances are 48% and 22% respectively, but if the pt's code was not observed, the chances drop to 21% and only 1% respectively.) Of course, those statistics would not mitigate the legal implications of a pt's death on this kid's illegitimate watch.
