Yes, Colby's pedigree quotes a marriage licence but I can't find record of the marriage either: this year range for Devon marriage licences is currently not searchable online. He also says that many of the names and dates for the Heywoods and Palmers come from a family bible.
I think the circumstantial evidence is strong that they are the same person; I've added a reference to Elizabeth Gayer's profile to a Chancery case involving the widow of Roger Gayer and a number of others who can be definitely identified as her step-children. The parties include Elizabeth Palmer, wife of Joseph Palmer, surgeon of South Molton. The parish records for their children and Joseph's burial all refer to him as Mr Joseph Palmer, consistent with his professional status.
Given his occupation, it may be that Joseph Palmer was not born locally? The son attributed to them, Joseph born 1706, is not in the South Molton baptisms with his siblings. Finding his baptism record elsewhere might offer some clues.