Where I got one of my undergrad degree's, there was an EMT class/program that was really involved in the surrounding community and at events on campus. They had great exposure and ride along's... things like that. I don't know how common this is among universities, but looking back, I wish I had been involved.
My feelings on the value of grades has evolved over time to the point where I am now, where essentially I advocate for focusing almost completely on grades. The reason why has a lot of components that I will break down. This will probably seem to ramble:
For one, an academic trail is the hardest to modify on the fly. Unless you have programs of study that are committed to grade replacement, you are stuck with what you get. In the case of PA schools, you sometimes see that retaken courses are averaged with the original grade, and you can get burned that way. I could belabor the point about grades, but to put it simply, the academic record you accumulate is expensive, a slow process, and frequently unforgiving. Grade struggles are something I've seen most frequently lamented among folks applying to get into a PA program. To sacrifice good marks is to sacrifice an advantage needlessly. When you are head to head with someone and competing for a seat with similar attributes to each other, the higher GPA wins. Folks chime in that things are never "equal", which is true, but you never know how well you will fare, so why not come to the table with awesome grades to cover your bases. You will want all the ammunition you can carry to the battle for a PA seat because often there are a minimum of 10 applicants per spot, and you have no way of knowing for sure how much firepower you will need to get your own.
So at the end of the day, it can take years and thousands of dollars to improve an academic record, but HCE can be obtained by hitting a for profit program and putting in a matter of weeks or months to your training. I have 2 areas in my background that would qualify me for the schools in the country that are the pickiest with their HCE requirements. To obtain my HCE paths, as well as the experience working in them, took years. Is it worth it to you to become an RN or RT just to get HCE to get into the programs with the highest HCE minimums? That's a handful of schools compared to the programs that don't care much about HCE, or else require very little. So in that regard, you still get more bang for your buck by getting high marks. Take it one step further, and if you are side by side competing with someone with similar merits, grades break the tie. Say I'm at University of Utah (a very HCE heavy program) interviewing with other nurses with backgrounds like mine.... I'm still going to want better grades.
So there's no scenario where I would regret not having great grades. However, since not every program cares about HCE like a place like U of U, I wouldn't want to risk good grades to obtain HCE. Taking the time to obtain great HCE might not be worth it due to financial cost, lost time (=lost income), or other opportunities for growth that you might miss out on. Sure, if you can manage to work as a CNA and get good grades, then by all means do it. But I just know how self centered employers can be. They wont care that you have a test in the morning and you haven't studied... they will want you to come in to work. If you want to work to get HCE, make sure you are the kind of person that wont struggle.
If that DO resident had followed his own advice to an extreme, he wouldn't be a DO resident. He probably could sense that you had your ducks in a row as a student, and weren't going to blow it if you relaxed a bit and got some HCE to round out your resume.