I have no idea how long BeachRescue has been an EMT. Let's use that as a jump-off point, and I'll try to not make it look like an attack.
Someone not in our line of work might think of it as a bad joke, like some LEOs (Law enforcement Officers) might make light of a bad guy getting shot in the butt. I am guessing BeachRescue is a new EMT, as the profile posted states (s)he wants to become a Paramedic and/or LEO, which makes me suspect BeachRescue is a "newbie" in the field, hence, feels it to be a funny story. If that is the case, BeachRescue will eventually become "seasoned", and know when to make jokes, and, obviously, when not to.
Sort of a case in point, is the old joke, the long time EMT and Paramedic having a discussion of a particulary gory call they did, in detail, not realizing they are grossing out everyone else at the Burger Barn restaurant where they are having the discussion (mea culpa, I actually did that).
As for the NICU/PICU nurse not taking action with the baby having convulsions and turning blue, I would have probably been loud and vulgar in telling her to get the f*** off the phone and do her job, or I'd see to it someone else more deserving had her job tomorrow.
Side note: an old girlfriend (former EMT) who had cancer (was a heavy smoker) has been emergency hospitalized for difficulty breathing, and a colleague from FDNY (mentored me when I came into the NYC Municipal 9-1-1/EMS system) was recently told her cancer had reocurred after more than 5 years in remission. Cancer, sure as hell, is NOT funny.