If "final say" is a recurring issue, then the team is doomed. The head coach cannot be responsible for the year long scouting process. That's not practical. BB had final say for years, but that stopped working once the brain drain reached a point that there wasn't general alignment there. He still had a strong personnel department whose assessments and valuations were generally aligned with his own.
Complete and total alignment 100% if the time is obviously not going to happen and sometimes it's going to be a truly divided room where someone has to say Player A or Player B but if that's a frequent fight you have to have then your coach and personnel guy are mismatched and one of them needs to go. In this case, it would presumably be Wolf so I guess Vrabel has "final say" in the organizational sense but for individual assessments the personnel side is probably in better position to make most of those calls. The personnel side needs to be evaluating and assessing under the same general philosophies as the coach though.
Maybe with BB it was the coach but BB is a special figure in football history. That is not the standard we should be going off of.