I am a strong believer in letting the member see how the union functions. After a member actually signs their union authorization card, the next great step of union participation in some member's lives is the filing of their first grievance. Bringing the member to the meeting insures a number of things for the union, management and the member. It usually forces the member to be candid with you about the incident prior to the meeting. That means fewer surprises at the actual meeting.
Management sees the member and knows the union is serious about the grievance.
For the member, attending the meeting clears up any doubt about the process being a secret one. Everyone is there and the cards are on the table. Now let's backtrack for a minute before you actually walk into that first level meeting. It is written properly and investigated. Deadlines have been met.