One may not believe rechilus even if it was related in public. The fact that a person is unafraid to publicly relate information that is cause for ill will is not proof of its authenticity and certainly not of its accuracy.
Furthermore, even if an accusation is made in the presence of the subject and the accused fails to respond, one may not interpret his silence as self-incrimination. The person may have been flustered and at a loss for words, of he may have chosen to remain silent rather than cause an escalation of the verbal abuse hurled at him.