That's not quite right as per CDC itself: https://www.cdc.gov/immigrant-refugee-health/hcp/panel-physicians/vaccination.html
So yes, as part of the exam they should go through the vaccination history and complete the form (and give a copy of the form to the applicant), but can't make a K-1 applicant take any vaccines if they decide they don't want any.
Vaccination Documentation for Nonimmigrants
The vaccination history of all applicants submitting for an examination by a U.S. panel physician should be reviewed and vaccinations they have previously received should be documented on the DS-3025 Form, even if they are nonimmigrants who are not required to meet vaccination requirements prior to travel to the United States.
Although refugees and K visa applicants are not required to receive vaccines before traveling to the United States, they must meet the vaccination requirements when applying for adjustment of status or permanent resident status in the United States. Therefore, for these applicants, panel physicians must complete a DS-3025 Form if the applicant provides reliable vaccination records. A copy of this form must be provided to the applicant for use as his or her vaccination record in the United States.