“Parallel construction is a law enforcement process of building a parallel - or separate - evidentiary basis for a criminal investigation in order to conceal how the investigation actually began.”
Police use parallel construction when they don't want to reveal their methods. I seriously doubt law enforcement would engage in parallel construction if it had access to iMessage but Apple asked it to.
That's exactly the case I was thinking about with my comment
1) Police don't care that APPLE doesn't want to reveal its methods, and
2) Unlike the Stingray, it wouldn't be illegal for them to use iMessage evidence in court if Apple provided it to them (especially with the use of a warrant!)
I think it's more about the police not wanting the public to know that iMessage is owned; having trusted-but-broken communication services is a serious advantage for them.