Some owners stay out of the way. Others, like Jerry Jones, are the general manager and make all the moves. Sometimes owners get in the way and meddle. Then you have the Arizona Cardinals with an owner with a specific skill set that makes him valuable in the evaluation process.
Team president Michael Bidwill is a former federal prosecutor and he gets involved in the process for character issues. He is part of the interview process at the NFL Combine and in other interviews.
When there is ever a character question, the Cardinals turn the player over to Bidwill and have him speak to him.