My guess is that the writing here is somewhat blotchy or exposes Coop as someone who makes mistakes. At one point I seem to recall Coop saying that James would have told us where the other piece of the necklace was to help with the investigation. James steals the necklace from the coconut in Jacoby's office and Jacoby has a heart attack and James gets caught with cocaine (Bobby planted) in his gas tank. Coop then demands the necklace from James. James tell Coop where he got the necklace, but omits the part about Laura Palmer giving it him or that he buried it in the forest. Coop then is astounded to believe that Jacoby has something to do with the case and gets all happy to get another lead.

Coop talks to Jacoby in the hospital and Jacoby explains that he was in the woods and saw James and Donna bury the necklace (making Coop look like he makes mistakes too).

 My personal belief is that Coop is exposed to the audience as a young know-it-all that really jumps to conclusions. Although Coop is somewhat the hero, the hero can't always be perfect. Lynch once again has done his job.

My opinion on this is based on a comment Donna tells James later in the series... Something like "We were the only ones who loved Laura, we have to help her because no one else will"... Their own personal investigation... Sure, James is afraid that they will blame him, but they release him inmediately, Coop makes it clear that they have nothing against him, yet he doesn't tell about the necklace and continues with his bullshit with Donna and Maddy... Why they didn't tell inmediately that Jacoby got the necklace? Why they didn't mention Jacoby's tapes?