I've had all sorts of varied experiences for myself and close family.
Situation 1) My dad was riding his bike, got some loose "chatter" (the blacktop fill that wasn't packed in the hole) that caused his rear tire to skid while he was headed downhill. Because his front brake held, he went end over end, first point of impact the top of his (helmeted) head. Some passerby saw and phoned 911. Police arrived and he was unconscious on the roadside, call went out for "next available ambulance". He didn't regain consciousness until he was at the ER, probably 20 minutes or so from the original time that he was injured.
Insurance tried to avoid paying because they said the ambulance was the "out of network" one. Well, my parents filed an appeal--turns out there was no "in network" ambulance, so insurance paid up.
Situation 2) My mom had a first time grand mal seizure. A couple freak elements made this even more serious. She'd been sitting at high table (the sort that has barstool height chairs) and whacked herself on the bridge of the nose on the table (or chair) on the way down, giving herself a severe nosebleed. Then her forehead caught under the toe-kick of the cabinet, so that her neck was in the position that all the blood was pouring into her lungs. Of course my dad called 911 rather than drive her (about a 15 minute drive from the house).
Situation 3) Oldest son passed out somewhere that had my work contact information. They told me the ambulance had been called, I requested that he be brought to the hospital that is my employer. The request was honored.
Situation 4) Ex (then still my husband) had a heart attack. 911 was called (I made him talk on the phone because I know dispatchers can glean info talking directly rather than talk to me, have me ask him questions, then relay the answers back to the dispatcher). They asked *me* which hospital, but said that they thought it should be hospital A or hospital B as hospital C wasn't the best for cardiac.
I also know that, when I worked in my prior job (I've been given new duties), I worked with financial assistance applications. The local ambulance company would honor our financial assistance (i.e., if someone qualified for 100% assistance, the ambulance would write off their charges; if they qualified for 20% reduction, the ambulance would do likewise).
On the other hand, I've pretty much always gone by private transport, but my situations were less serious. And triage really doesn't care how people arrived--they evaluate based on the particulars of the situation (although I will say that there are few things scarier than hearing people being paged to come to the ER "stat" when it's about *you* as the patient). In that particular case (really horrific miscarriage with major hemorrhage), I even bumped the stabbing victim the police had brought in just before me, even though I'd walked in thinking I was just fine (until I stood up from triage and there was a 3' diameter puddle of blood at my feet).
In the end, unless you *know* the situation is something that isn't a true emergency *and* know how to handle the situation, I think that it is the right decision to call the EMTs. I wouldn't want to live with myself if I'd just sloughed it off because "well, it's not really that serious" and I was wrong--I don't see anything in the OP that suggests that the people who called 911 knew that the student had an existing seizure disorder beforehand.