I can offer a more start-up-ish perspective. When the original startup I worked for was just starting to grow, everyone in the team was part of the process. We all got to spend time with the candidate and work with them. At the end of their trial day with us, we were asked: would they make a good match / fit for the team? Since we were still in smaller numbers, what mattered most is if new starters would get along well with those of us who have already been working there.

As the company grew bigger and became more than a startup, the non-HR team was less of a part of the process, but still slightly involved. We still had trial days with each candidate (if they had made it that far in the process), and again, the final word depended on whether or not the existing members of the affected team felt like they could work with this person, or that this person would be a good fit for the team.

While this is more HR than recruiting, from my experience it's truly the soft skills that get you hired. Everything else technical can be taught and learned.