So this specifically relates to Section 3 of the 14th Amendment, which doesn't say that a person needs to be convicted of anything to be barred from office. This section was specifically inspired by a need to keep people who supported the Confederacy out of the government, and the precise issue of whether or not a conviction of anything was required for disqualification is a matter that was studied by the Congressional Research Service. They had this to say, quote, Section 3 of the 14th Amendment does not expressly require a criminal conviction, and historically, one was not necessary.