Not sure if anyone actually said it, but... good on you, Todd, for seeking some fundamental first aid training. Even things like the AED in the food court at the mall now mean something. Hopefully, you'll never need this stuff, but in truth, you probably will. Wish more people were willing to man up. I think it's awesome that you're thinking this through, and putting real-world application to it.
... as she had to. She'd be negligent to teach you things that are outside of the scope/protocols. The First Responder level is precisely what it is - fundamental ABCs - not med-surgical stuff. That's no slight on the cert - every paramedic worth a damn knows that a good FR or EMT-B is a HUGE asset. It's not high-level, though, so only the basics are taught. Some of it, as we've been discussing, is lagging behind the change curve.
I don't know if PHTLS or ITLS require you to be an EMT-B (or higher), or if a first responder can take the class, but it is a good thought. (EMT-B is also a great course - if keeping that level of cert up here wasn't a giant ass-ache, I'd go back just 'cause...) There is a ton of "alphabet soup" here in the medical world as there is anywhere... Things like ACLS and PALS aren't going to be useful to you (both advanced life support stuff with all the cardiac meds and whatnot). I was going to strongly suggest BTLS (basic trauma life support), but then realized that it had evolved into ITLS. That class was a challenge - had some tough instructors - but it was very, very cool.
Regardless, it's not something YOU should do, unless you advance your training and are operating under those protocols, or have no recourse but an exception. It is, however, great to be familiar with what SOMEONE can do, and who that someone is and can be summoned if needed. You obviously know this already...