I think it's a reference to Sherlock Holmes fandom. "Watsonian" means looking at something the way that Watson would have done -- e.g. we're talking about something from within the framework of the universe. "Doylian" means looking at something as author Arthur Conan Doyle would have done, e.g. from outside the framework of the universe.

So talking about why Sam and Dean have the relationship they have is Watsonian, while talking about why the creators of the show make their decisions is Doylian.