No you didn’t misunderstand. Your interpretation is exactly right— because that is exactly what happened. Any other reading of that scene is obstinately blockheaded.
Rin is trying to inject more heart into the team this way… instead of picking by time alone, he basically summoned the people who WANT to be in it.
Seems to me like before, if someone had the best time then they would get placed on the relay team— perhaps whether or not they even wanted to be there. Now Rin is saying, hey— I’m not going to make you do this unless you REALLY want to be here. Because the event means a lot to him.
Multiple times in the episode they showed a contrast between how Sousuke does things (commenting on Ai’s poor timing, etc) and how Rin approaches swimming (“Hard work beats talent” “You swam with your all, Sousuke.”). Now Rin is going to apply that to the whole team— showing that he cares more about their feelings than whether or not they make the grade alone.
And that’s basically what happened to Rin at the end of S1— Seijuurou took him off the relay team, not because his time was bad, but because his head wasn’t in it and the team would’ve suffered.
There’s actually a cool quote from Ian Thorpe (Australian Olympic gold medalist) about the relay
This is why relays are so important, because you can find more in yourself for someone else, than what you can ever find for yourself.
And I think this is what Rin’s decision encompasses.
Seeing this whole thing any other way is downright obtuse.