Quite honestly I don’t ever believe parents like that. Most actually concerned parents don’t go as public with it. Usually there is an ulterior motive behind it.
This case should be very easy to prove or disprove Have the parents just produce the certificate. If the parents can produce the certificate, then I think at that point questions need to be asked to the teacher by the principal. If the teacher denies giving the kid the certificate, then ask the kids in the class.