Christ applied this to believers in the church. Accusations are not to be accepted or pursued without prior corroboration. Adjudication in the church, even in cases where a vindication results, can do real damage. Elders are to be protected from such harm to their ministry by a prior examination of evidence. Paul's purpose was not to protect wrongdoers in the church, however.
Evildoers can use their position as a shield of privilege.
It is an evil thing to allow any justice system to be used as a means of avoiding justice itself. If the harm to the church by false charges must be carefully prevented, so too must clerical privilege. Those who do sin must be rebuked publicly. Paul's purpose was to protect the innocent, the congregation, and the ministry, not evildoers. Paul thus warns Timothy of the gravity of his responsibility and that of the church.