Which part?
I've been involved in TBIs in the field and have been to some of those bases and evacuated guys in some of those direct manners.
You get injured there are reporting requirements at different levels. Usually all evacuated service members are going to be immediately notified up the chain to the brigade level immediately but there is ongoing personnel tracking in the human resources and operations side that would run it up outside of medical at different rates. Immediately, daily,etc
Rockets come, explosions happen, we all good. Then private snuffy starts showing concussion which is just now being recognized as a mild TBI. You get brought to a medic or aid station that might have a PA or doc. They do a MACE exam (referenced in the interview). They assess yes this is a concussion. It goes into a battle field injury roster and that is reported daily and weekly in different formats up the chain of command. Certain things (life limb eye sight) would have different reporting requirements and their evacuation process would trigger higher echelons of reporting.
In this case, this being a very high profile event, I don't doubt that the information was not being pushed up from the bottom...rather it was being pulled from the top. They know the question are coming. So they make the ask after the attacks, "everyone good?". The aid stations report they have seen NO patients. Then hours later or the next day private snuffy who is trying not to be a wimp tells his first line leader, "sarge, my head is killing me and I'm naseous". Or they go to the sick call the next am at scheduled time. That might be the first contact for something that could trigger an injury reporting. You then start managing them and if you need a CT scan (not always needed but there's pressure here too so all of the sudden the docs are evacing anything that might get them burnt if they miss it ) they are getting evac'd to germany. Medevac flights cost about 300k per plane and the seats are assigned in order of need. So it is common that you could have 15 injured but half go on one plane and half on another. A continued concussion without red flag signs is not an emergent transfer.
The rest of the interview is politicking about whether some pentagon peeps knew in one meeting but said they didn't. And of course, there's the political piece. If you say Iran injured no one you are doing both countries a face saving maneuver. US doesn't have to blow Iran up. Iran gets to brag about their glorious attacks. We got some concussions from sniping their high ranking general guy? The pentagon SURELY wants the media to stfu to avoid a diplomatic crisis becoming a full hot war under media scrutiny...or Trump admin has to back down like bitches, which they don't want to admit doing. So all that stuff is just me watching politics, not actual military doctrine.