The difference, of course, being that this isn't a life/death situation. This is a professional sports team. Also, holding up the Navy Seals as the #1 Performing Org in the world is a bit misleading. They are an elite team at achieving military goals. In terms of Sports, you'd probably look to the Patriots as the elite team of achieving sports goals, and they have dipped heavily into the low character end of the pool to get franchise success.
So, while you may want to have higher, to use the videos terminology, "Trust" Guys as your leadership group,, there is no problem with having a high performance, low "trust" player as part of your team, as long as you don't make him your captain. Patrick Kane is the perfect example of that. Low quality person all around, Conn Smythe Winner.
If you want to talk about building your leadership core, you absolutely want high character players, that is more important than them having high skill, though I think having your leaders being a productive important part of the team is still.