From Dallas Morning News:
“This is the first movie I’ve made that he hasn’t been directly involved with, although he was around as a friend,” says Anderson, above at Cannes, who became good buddies with Wilson at the University of Texas shortly before they made their first feature, Bottle Rocket. “We started out doing this stuff together in the first place. It’s a family dynamic.”
The good news: Anderson’s current script in progress, a large ensemble piece, has a part for his old friend, and Wilson says he’s in.
From an Owen Wilson fan site:
“It’s not weird to not have him around because there is so much going on and we had such a strong group of people. But, at the same time, I love working with Owen. He had read the script and given me some advice about the script, along the way, and he saw various cuts of the movie, so I had his voice in the mix. This is the first movie I’ve ever made that he does not have a credit on, in one way or another, and often in more than one way. I don’t expect that’s likely to happen very many times.”
On why Owen Wilson isn't in Moonrise Kingdom:
Wes Anderson: "It's always tricky for me. The part that Edward [Norton] plays, Owen could have played that part. I think it has some similarities to parts Owen's played in the past, and I've always wanted to work with Edward. But I do feel like Owen and I are so connected in our careers, it's almost tricky for me not to have him in the movie. I miss that. But Owen was a very valuable counsel for me. We read various versions of the script and saw the movie more than once while it was in progress, so I always feel like I've got his voice in the equation even when he's not directly involved."
So while Anderson doesn't explicitly state why Owen Wilson didn't play a visible role in the development of the film, he does note that Wilson was involved in a more passive role as a friend. The about.com article also hints that Bruce Willis' involvement in the film might have come about through Owen Wilson.
Anderson's next movie (mentioned above) does feature his friend.
FWIW, I don't believe that the other Wilson brothers have been involved in any Wes Anderson project that isn't based on an Owen Wilson (involved) screenplay.