Dad Joke Slipped out during Ride Along

I did my ride alongs for my EMT Class in a 12-hour shift with a professional (Non-Volunteer) Company where everyone does at least Fire 101, Fire 102, and EMT-B. My preceptor was a parademic and seemed pretty jaded for being so young (important for context.)

We had a call for a 19yo male LoC. We get there and he is sitting on the couch. Looks fine. The unit driver (EMT-B) takes his vitals. All normal. Apparently this kid cut himself and fainted from seeing the blood. Tried to get up, saw his bloody hand and fainted a second time. He vomited and siezed between fainting 1 and 2. My preceptor (a young medic) wasn't even going to do his vital because he looked fine. He chose to not goto the hospital and we got a sign-off. This kid is only a month younger than my oldest son, and seeing him shaken up turned on dad mode or something and as I was leaving I said "Try to keep your blood inside your body, yeah?"

The kids thought it was funny but I feel horrified that slipped out with a PT.

My preceptor or the driver didn't say anything except making fun of the kids for being dressed up like cowboys and freaking out over a little blood. I know compartamentalization and all that but I feel like an asshole.

Is accidently being a smart ass part of the job or do I need to just not be around PTs?