This is a Rule that saves your butt once you are hired. It also applies while you are in the interview process too. You just do not want to reveal anything more than what they are asking. Control of information is key. This does not help you bond with the people with whom you are or will be working. Anything you say can and will be used against you. So, be careful. Anything you say can and may be misconstrued.
As with naming a salary figure first, whoever opens up first loses. Let them reveal everything so you have leverage. Especially do not talk about how awful your current or previous companies have been in the interview. They should not ever hear about this – not even after you have been hired. They like to think they're getting a diva or the prom queen; tell them how much you loved your old company and how you're still such good friends with everyone and you often go out to lunch with them still. That shows that you have a good enough personality to stay hired anywhere and that puts a secret fear in some of them that you may go back if your old company asks.
Remember, the company has most of the leverage financially, but there are still things you can do to maintain an independent stance despite that leverage. There are only a couple more things to remember about this Rule. Although you should not disclose everything before you get a job offer, you cannot lie. Do not claim a degree you do not have, certifications you never achieved, or a job level you never worked. Now, while they cannot check everything, it is easy to verify degrees, certifications, and credit history. So, be truthful – but guard that truth carefully. They are only entitled to it on a need to know basis – if you feel they need to know.