If Luca Brasi was so reputed to be loyal to the Don, why wasn't he ever officially a part of the Corleone "family"...or was he?

Did Don Vito not trust him enough to let him join his family?
I don't recall anyone in the top brass of the family mentioning him in that capacity.

It was the nature of their relationship, it seems to be a professional one (albeit with friendly "respect") between the two.

Vito probably knew Luca's past and probably didn't want his family getting to involved with Luca, he was clearly a psychopath.

I'm not sure what you mean by "officially." What would make him official? Other than frequency on screen, how was Vito's relationship with Luca different from his relationship with Tessio or Clemenza?

Louren, I'm inferring that you see something in the seeming arms-length relationship twixt Vito and Luca that suggests something other than family membership:

Luca was "special": he reported directly to Vito, who gave orders to him directly, rather than through Hagen. Luca also seemingly didn't have an organization reporting to him. The novel explains that Luca's value to Vito was that "he could do a job of murder all by himself." He made the Don nervous because, according to the novel, "he was like a natural force, not easily controlled..." That would explain Vito's stand-offishness. Also, it wouldn't do for Vito or any other member of his family to be seen too close to a guy whose main occupation was murder. It was enough that the other Mafiosi knew about--and feared--Luca's loyalty to Vito.

What TB and Olivant said..

Also the novel states that "Luca was in himself one of the great blocks that supported the Don's power structure".

Nobody but the Don could tell Luca what to do.

Exactly. It is really telling that Sol made sure Luca was dead. Recall when he thought he'd killed Vito, he instructed Tom to talk to Vito's sons and his capo regimes, and Tom said he would but added that even if he convinced them there would be no stopping Luca Brasi.

He lacked the social skills to be a capo regime, but he was the family's ace in the hole....or so they thought.