When an employer is trying to recruit/hire a candidate, there are obviously interviews scheduled so the employer can learn more about the candidate. Those interviews are generally with the people most closely related to the position that's open. The position's supervisor, someone from HR, someone from the executive suite (or owner) and perhaps a peer or two are the typical picks.
The candidate, especially a top performer or one who wants to control their career growth and direction, often wants to meet others in the organization (by title). I encourage this. It's one thing to "get the pitch" from those closest to the position, and maybe feeling the most pain with the position being open. The story might be completely different when talking to someone from another department, or others related to the department in question, but not "hand picked" by management.
Employers invariably have their most articulate and enthusiastic employees participate in the interviewing process. Employers want people who seem happy and can tell the story (and maybe who walk the line) to meet potential new hires. These same folks could also be the "favorites" of the boss, or maybe haven't been at the company long enough to have a real sense of the environment, culture, management style, etc..
I think it's a good idea to give candidates the option to meet a couple of people of their choice, especially for higher level and executive positions. Letting the candidate choose who to meet in the company more fully involves them in the process, makes the process more effective and transparent and makes the candidate feel more personally involved. All of those results are good. I don't know why candidates don't ask to interview others in the organization, and I don't know why employers don't offer the option more frequently.
What's the worst that could happen? The candidate might find out some information that wasn't intended for them to find out. Perhaps they can "feel" more realistically what the employer culture is really like, as opposed to what's being presented. The result might be that the candidate decides not to pursue the job for personal reasons.
Isn't it better to find out in advance that the position wasn't really right . . . for whatever reason? Hiring always involves risk. It would seem that the more information gathered by both the employer and the candidate, the better. The candidate deserves the chance for ample due diligence, just as the employer does.