He was invited to the wedding, but Brasi knew that he wasn't necessarily welcome for the ceremony. That's why he was practicing his speech off in the corner. He was trying to show his gratitude to the Don and his family while personally giving the gift directly to the Don. He knew that he wasn't part of the family, but he was a part of "la familigia." Also why the Tattaglia's sent him to the fishes. They knew (or suspected) his ultimate loyalty lied with the Don. They had a perfect opportunity to get him out of the way. The fact that Brasi was just as terrified of the Don as the Don was of him is the perfect nuance.