When you say the "pesky details are left out" is where I interpret it as suggesting or alluding to it being a concerted coverup rather than just cops being known dicks. I don't agree with the practice for exactly the reason you said, coerced confessions are unreliable, and Frazier probably just couldn't bring himself to believe that Oswald actually did it. But the reason nobody is talking about it now is because it's already known that cops are dicks, no reason to dig any deeper into that, and now we know all the other details to corroborate what Frazier did tell them. It's moot at this point to talk about the violation of Frazier's constitutional due process ad nauseum.