I'm going to say yes--to some degree, but to determine what "true" is, may be subjective to our own moral ethical standards...
I think one reason it is called True Detective is because is playing on True Crime.
True crime is a non-fiction literary and film genre in which the
author examines an actual crime and details the actions of real
people. The crimes most commonly include murder, with tales of serial
killers dominating the genre (about 40% in a 2002 survey), but
true crime works have also focused on other subjects, for instance
policemen memoirs, and more recently reality police TV shows.
Depending on the writer, true crime can adhere strictly to
well-established facts in journalistic fashion, or can be highly
speculative. Some true crime works are "instant books" produced
quickly to capitalize on popular demand; these have been described as
"more than formulaic" and hyper-conventional. Others may reflect
years of thoughtful research and inquiry and may have considerable
literary merit. Still others revisit historic crimes (or alleged
crimes) and propose solutions, such as books examining political
assassinations, well-known unsolved murders, or the deaths of
celebrities. Although the genre examines real historical events, true
crime TV series typically use reenactments to help draw in viewers.
However, over the years the more traditional view of True Crime being solely non-fiction has somewhat changed and is now used within genres of fiction with stylization (realism, hard boiled), execution (memoir-structure), tone (serious), and themes (us against them/me against the world)...And this matters because the juxtaposition to fictional true crime, then lends itself to the questioning of what is "true-crime" itself?
Fargo (the film and tv series) for instance, is a dark comedy crime drama, and presents itself as story of "True Crime". The reasons for that are both the ideas that is funny to assume that events in real life would ever actually happen this way, as dark comedy lends itself to farcical plots/tropes, but also because Fargo still executes itself in a serious dark crime-drama manner, with it's own characterizations of realism, and does have decent (usually detective/police) characters with integrity, fighting against people whom are often criminally insane. (There are grey characters too, though) However some of the crimes or plots Noah Hawley has used in his TV series, do sometimes come from "real" crime stories in the Dakotas/Minnesota area--so there in fact are elements of real 'true crime'.
True Detective then follows suit in some ways, because it is a dark/gritty FICTIONAL Crime Drama, but it does present a RUSTic-realism reality and is looking more inherently at the nature, behavior, or psychology of people involved in both the crimes and law enforcement, so I would agree with you it is in fact asking, "What IS a true Detective?"
TD's creator has insisted that there is no supernatural phenomenon, but I think by definition a person can still argue that TD, especially the first season, does have magical realism elements, meaning it does at times look like supernatural things are happening, despite that, in this case, there are also "real-world" explanations for all of those things. Magical Realism is also tricky genre to define because you have works like A Hundred Years of Solitude that relies on an unexplained idea that somehow, someone can exist further than a lifetime or something like Mark Helprin's Winter's Tale that is set in a very realistic period-New York City, but is sprinkled with fantasy elements and both are considered magical realism...
(Note: Another example of something similar to True Detective or Fargo borrowing on 'True Crime', might be Longmire, albeit with Native American magical-realism elements sprinkled through a rural-setting, featuring the concept of the dying cowboy and historically unresolved Native American conflicts.--Also Dana Gonzalez is both Longmire's and Fargo's cinematographer)
But one reason True Detective would want to use that genre, was again to home in on examining the nature of these characters and their reality--and decide what or whom is "true" and how "true" can be antiquated with either good or bad and how complicated those ideas really are when we are looking for hope from damaged people. Both main characters, Rust and Marty each have their own problems and those problems affect how they investigate, but argumentively I think the series tries to make the case that as flawed as they are, they're still pitted up against something that comes across as something more evil, then their own predispositions. And I think the same case can be made for second season characters, despite I feel like it's somewhat philosophically opposite/challenged to the ideas the first season purposed in Rustian philosophy....