There were blanks on the forms for listing parents' names. For a sample marriage certificate from 1920, see:http://homepages.rootsweb.ancestry.com/~balzarm/images/theo_...
Whether the blanks were filled in cannot be known without ordering the certificate.
Wisconsin vital records post-1907 can be obtained either from the Wisconsin Vital Records Office:http://www.dhs.wisconsin.gov/vitalrecords/
or from the county Register of Deeds:http://county.milwaukee.gov/VtialRecordsSystem9855.htm