One of the problems that detectives investigating complicated murders have is that there is all sorts of evidence that probably exists which it would be convenient for them to have which they don’t. It would be great to have a recording of every phone call every suspect made, for example. Better still would be 24/7 surveillance footage of all suspects. Of course, these would make for very boring detective stories, so no detectives have these.
There is an intermediate case, though, which is the police; the police have broad powers to obtain evidence which ordinary people cannot use. Police can get phone records, they have a network of people to track the movements of an individual, they can compel banks to give them bank records, etc. Sometimes the detective has these advantages because he is a police detective; sometimes he has these advantages because he has a friend on the police force. Perhaps one of the more creative examples was Lord Peter Wimsey, who was able to obtain all sorts of privileges because of his prefix.
There is a curious interaction of these special privileges with the fair play principle. Of course, strictly interpreted any such privilege is fair play if the reader is given the same privilege by being given the information that the detective is, but in another sense this violates part of the spirit of fair play because it takes from the reader the possibility of imagining himself doing what the detective did, under similar circumstances.
This is, for all its flaws, one of the great triumphs of Encyclopedia Brown. His proofs are often pedantic or trivial, and occasionally factually incorrect, but they are all proofs that anyone who has read a lot of non-fiction books could make. The glory of Encyclopedia Brown is that, allowing for the fact that in real life no one would go to the Brown Detective Agency, anyone who reads the books could open their own Brown Detective Agency and make a go of it.
I should also note that I think that this is one reason why some detectives resort to criminal means (more generally, things unavailable to the police) to obtain evidence. This is, essentially, a sort of special privilege for the detective. I suspect this is one of the reasons why I think that such behavior—and, in a sense, lying to witnesses to obtain their testimony—is not as good as the alternative. By doing things which the reader cannot or should not do, the detective gains special privileges which help to explain his special success.
I do not think that there is anything wrong with a detective with special privileges—there have been many great ones—but I think that the great detective without special privileges is a difficult ideal worth being aimed at, at least.