Not sure if it's been said or not but memory is a tricky thing. Our memory of things over time can evolve so two people remembering the same event will have different stories. Also the power of suggestion has an affect on memory. Maybe he told the story to someone in the past and they asked him for clarification "so he was in the water and you had to swim out to save him?" even if he said "no, he came in after me and I took him to the hospital", his memory could have been shaped by that question. Brains are very interesting things. Anyways, it doesn't mean he is lying, just that this is his memory of the event now (even if possibly it is wrong).
I guess the question is why he is sharing? Maybe he misses his bro, maybe it helps to talk about him, or maybe he likes the attention.