Reporting in first person singular where two authors are listed I am proofreading a text where two authors are listed (one of which is the writer, and the other, apparently, only a "supervisor") and in reporting the author(s) use first person singular (instead of first person plural): I believe, I was surprised etc. I find this very illogical and was wondering whether there was a rule for this type of situation.

To be more specific: right below the title of the essay two authors are listed. However, in the introduction and in the conclusion, the author(s) say that "I was somewhat surprised..." and, towards the end, "it is hard for me to..." It seems illogical to me to list two authors and then report in the first person singular. When I suggested this be edited, they told me only "one person was the writer, while the other one was the supervisor". 

What should be done in such a situation? Should the "supervisor" also be treated as one of the writers and verbs be written in plural, or should this person simply be removed from the list of authors regardless of his or her contribution?
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.