I think the navy seal/olympian stuff is a little overblown. Yeah, that stuff will get you places because it makes you extremely unique and amazing, but like 5% of a T20 class has that sort of stuff. And even then it's not like navy seal, it's more like a couple of them are veterans, and its not olympian, but more like one or two were D1 athletes in a non-premier sport (i.e. not baseball/football/bball) and maybe a few m DII/DIII. I probably met like 100 people at different T20 interviews where many of them ended up very successful (i.e. multiple T5 acceptances), and nobody had the super crazy stores, and only a few had the more conservative versions. Once in a while there's a Johnny Kim, but they're just so rare (hence why they are prized so highly). But the meat of a T20 class is just people with good grades/scores and some semblance of a story and ECs to match, like oh I'm really into neurodegenerative disease and alzheimer's research, or I'm really into working with underserved communities. This is especially true for anyone coming straight from undergrad, since you really don't have time to get really out of the box.
There are a couple different explanations for the scarcity and confusion on part of top applicants. I think the hard part for applicants to wrap their heads around is how small the classes are. It's not like undergrad where programs are admitting thousands of kids, and there's sort of a general threshold that you pass, and if you do, you get accepted. If you're looking for a class of only 100, you can really get into the nitty gritty of each person and "build your class" around having a nice distribution of everything.
Think of it like making a football team - there might be that crazy gadget player, and you definitely want one of those on your team (like the unique story people). But a way larger chunk of your team are going to be linemen, who are a completely different type of athlete. The thing is, you've got to be the best at your position, and you're compared within. So yes, being 6'4" and 295 is great to be an LT, and you could probably play. But if a team could have anyone, why not take the guy clocking in at 6'6" and 330? Basically, if you're sort of meat-and-potatoes type applicant, it's not enough to just pass the threshold/class average - if you're about numbers and checking all the normal boxes, you've got to be impeccable because you're balancing the average out with the spicy applicants who might not be toting numbers as impressive, and a bigger chunk of the applicant pool is directly comparable to you. For example, you might be a research heavy neuro type person and a traditional applicant, and totally pass the T20 II/acceptance threshold. But if there are a some people with grades/ECs/essays a smidge better your cycle, you're going to get passed over unfortunately. Just like in a lineman heavy draft year, you might get drafted lower/paid less than you otherwise would.
The other big things would be a consistent and demonstrated interest in research. And then leadership of course, given the missions of these schools.