If you convince them that you really are X and they give you the file, i think that would be considerd fraudulent. Whether or not an injury takes place to raise it to the level of fraud i guess depends on what was in the file, but in countries with strong privacy laws, someone would probably be in a heap of trouble.
To be able to login as BoBibbidyFooBar, and subsequently access ANY company's info in the system without changing their identity from BoBibbidyFooBar does not, in any way, constitute any sort of fraud. It literally cannot, by any sensible definition.
Not at all because what you describe involves impersonating someone else.
In the OP case, they were authenticated in the session as themselves and always acted under the truthful identity and asked for a document and access was granted.
So the analogy would be going up to the desk and saying: I'm John Doe, my id number is X (truthful value), could I see file ABC? And the attendant checks that id==X does have access to document ABC, and thus hands it over.
A better analogy would you asking for your files, and then the secretary taking you to a filing cabinet containing everyone's files right there with yours. You don't have to lie about who you are, you can just look at other files because they're right there in the place that you were just given access to.
Analogies are always going to be imperfect, but I can't see the argument that the "separate request" analogy is any worse than yours, let alone "wrong".