It's a simple thing really. That really isn't a hard question. Consider when political maneuvering erupts into major arguments. The answer is an easy one, it doesn't. Such behavior masks real issues while setting up walls between different sub-groups in the organization.
People stop talking to each other and the organization falters.
Contain rumors by talking to the person you would otherwise be talking about. Insist that others do the same. Ignore complaints about yourself and others that come through the grapevine. Only direct complaining is acceptable. No problem is so great that it cannot be talked into submission in a calm and professional manner with all those involved.