It's by and large a cooperative process between your lawyers and the opposing party's lawyers, but its not really voluntary. If you refuse to answer a discovery request, opposing counsel can go to the judge and get a subpoena compelling you to hand the documents over. Hanging over the whole process is the threat of sanctions: for your attorneys as well as for the company. For your attorney, it is a violation of the civil rules of procedure to unreasonably refuse production requests, and it is a violation of the ethical rules to not hand over documents that are relevant and not privileged just because they might hurt your case. The former can result in sanctions, and the latter in disbarment (i.e. the professional death penalty), so while your lawyer loves you and is on your side, he will cough up the documents the other side requests. If the client refused to cooperate, the court can hold him in contempt as well.
It sounds like the penalties are severe if you are detected making omissions during discovery - but how would that actually be detected?
At the most basic level, the system is built on trusting lawyers to act dutifully as officers of the court. Corporate law firms care very much about their brand for trustworthiness, because at the end of the day their business depends on that brand. Nobody wants to be like Arthur Andersen, which went from a $9 billion company to nothing because people stopped trusting their brand (for the actions of a relatively small group of partners).
Are you really saying there's no independent auditing? That the entire system relies on Best Buy's lawyers incriminating their co-workers and the employer who puts bread on their table? That seems exceptionally trusting in lawyers' professional ethics.
Does the discovery at least have to be done by an different law firm to the corporation's day-to-day legal work?
Remember also that plaintiff's counsel also thoroughly interviews witnesses under oath. Cross-checking witness accounts can highlight inconsistency in the documentary record. It also adds a second group of people who don't want to hide information under threat of punishment.
Boy, you're sure a glass-is-half-full type, 'rayiner --- my experience in litigation was that:
1) many, many litigation attorneys like to play chicken, doing their utmost to obstruct your discovery (or to demand unreasonable discovery for themselves), stopping just short of making you so mad that you go to the judge; and
2) the vast majority of litigators hate going to the judge, knowing that most judges utterly loathe discovery disputes and basically absent themselves from the discovery process unless they absolutely have to get involved. (There are exceptions; some judges announce that counsel can get them on a conference call just about any time they're not actually on the bench --- not surprisingly, those are the cases where counsel can actually be pretty reasonable ....)
Edit: I was on my mobile and I couldn't confirm this. In fact, as the peer comment said, when it refers to the litigants the process is discovery. A subpoena is required to compel a third party to testify or provide documents. Discovery is normally just a give and take, unless one party objects and the court intercedes.
Here you go: http://en.wikipedia.org/wiki/Discovery_(law)