Reporting in first person singular where two authors are listed
Number in scientific writing is fairly straightforward:


Multiple authors should be plural.
Complementarily, a single author should be singular (except when speaking of author and reader together), but many academics are uncomfortable with this and end up either sort of doing a sort of "royal we."


The response of the authors seems to be asserting that the supervisor is not really properly an author.  As such, I would suggest pointing them toward the Vancouver Protocol and giving them a choice:


If the supervisor is really an author, the paper should be changed to plural.
If the paper remains singular, the supervisor should be demoted from authorship to acknowledgement.