I agree with you KK, but I just can't see an 18 year old Adnan not trying to take Jay down with him. He would have to be pretty calm to say "This likely won't benefit me, so I'm better off playing dumb and letting Jay basically get off free." Though to be fair, he may have thought there wasn't near enough to convict to him anyway and once he was convicted, there was no reason to change his story.
I agree, but it is helpful to remember the order of events and the motivations of each party:
1) Adnan gives the rough outlines of his alibi to police the day of the disappearance
2) Jay is questioned later, giving him opportunity and motive to confess & betray
Jay: Once he pins Adnan, he implicates himself, but he sets and controls the narrative. This is the prisoner's dilemma. It is all about risk and reward. Jay had to assume that Adnan was going to set him up for this, and he pretty much uses this reasoning in the police interviews. It provides a nice bow on his own motivations as escaping being the patsy for Hae's murder. With the details Jay provides the prosecution fixes its eyes on Adnan using the motive of a lover's quarrel. Jay plays his strong hand and wins.
Adnan: Either he was innocent and gave a completely truthful denial he was involved, or he denied he was involved to prompt increased scrutiny of Jay. Remember, he doesn't know Jay was going to blame him for everything when he gives his first statements to the cops. He would have to re-cant at that point and admit involvement. The benefit of doing that just seems so obviously skewed against him. It is really hard to tell the level of each party's involvement, but it seems like Adnan was involved enough to realize that admitting to his involvement means that he is going to jail for life with only the possibility of parole. He had a weak hand to play, but raising the stakes of admitting he lied and attempting to implicate Jay seems like a sure loser.