Don't rely on other students.
Contact the ROO or PMS...
Agreed, but I'm not a "other student" I actually obtained my EMT certification, concurrently while in a pre-Med program.
Reasoning for my "forget it" above. If your son REALLY wants to be a paramedic, the Army officer route is probably not ideal. Paramedics in the military are often seasoned and highly trained combat medics, corpsmen or med-techs in the Air Force. These are all enlisted folks who work along side doctors, nurses and even pilots flying planes/choppers. Most LOVE what they do and some go on to be nurses, doctors or PAs.
Without looking at his specific program, I cannot comment much on his chances at the ROTC battalion at his school. However, I did look at one very fine school in Southern Alabama who is, in my opinion, pushing the edge of the Emergency Medical Services scope. I also looked at two other schools, one without a ROTC unit, the other with an across town offering. All of these schools offer a BS leading to a paramedic certification.
The school w/o an ROTC offering lead to a BS heavy in Chemistry (think Pre-Med here) and I imagine with careful tweaking of the electives, going on to Medical School or PA school could be an option.
The issue here is generally ROTC is training for the combat arms and combat support roles. There is a sub-set of ROTC for nursing students. And a small amount of ROTC grads do go on to branch MSC or Medical Service Corps, think support or very special allied health roles (Supply, Logistics, Admin).
If your son really wants to be a Paramedic, he'll not be able to practice his role fully as an Army officer. Even if he branched MSC, the Army would expect him to stick to his role or training the Army needs, as it already would have plenty of superb combat medics.
Here's another kicker, if he wants to serve part time, and practice as a paramedic full time in the civilian world, that would work. I've seen this personally as a reservist. He could be literally anything in the Army Guard or Reserve, even a high speed infantry officer and STILL be a practicing paramedic. The sky is the limit so to speak for part-time Army officers. I've worked along side Psychologists, Pharmacists and Pathologists, all in the Army reserve and practicing their craft out in the real world. Hardly any went through ROTC.
There are many scholarships for Army Reserve/Guard ROTC students. Dad is right, talk to the ROO about these. Many go unused according to my son's ROO. Any way, best of luck to your DS, he will find a way, believe me, mine do, LOL!