Lenny, if both spouses are agreeable to getting divorced, there is no shaila and any beis din will grant the Get (often after first discouraging it in an attempt to save the marriage.) The only time it becomes a shaila (or, rather, a beis din trial) is if one spouse wishes to continue the marriage (asking for “shalom bayis”) whereas the other spouse is insistent on getting divorced. In such a case the default halacha is that the beis din cannot grant the divorce unless the spouse petitioning for it provides proof in beis din that he/she was wronged by their spouse in a manner that halacha specifically recognizes them as becoming entitled to a divorce.
The circumstances that halacha recognizes as entitling a spouse to a divorce are very limited and very specific. And alleging them is insufficient in itself to allow beis din to order a divorce be granted, even if the party sounds believable. To take an extreme example, the Shulchan Aruch states that if a wife comes to beis din asking for a Get and says her husband physically hits her, the Mechaber rules that the Halacha is that beis din must give him warning that if he doesn’t stop hitting her they will require he divorce her. And if he continues being violent beis din can and will require he divorce her. But that is assuming she either proves he is violent (i.e. witnesses) or he admits it. But the Shulchan Aruch specifically says that if he denies her allegation of violence, beis din cannot accept it at face value to mandate a divorce. The Shulchan Aruch rules that beis din must place an agent of beis din in the marital home to witness the violence before halacha will permit beis din to mandate a divorce.