But what I wonder is how they circumvent the entire trust mechanic when the phone is locked. When the phone is locked most of the storage is encrypted too.
I've always thought the way to deal with this is to use a OTP scheme. If you have a one time pad that's as large as your data set (assuming we're talking about some reasonably small number of critical documents here), you could generate the cyphertext from your key and then generate another key that translates your cyphertext into something innocuous - grocery lists or whatever.
There's no way the court could prove the key you gave them isn't the right key.
It would only take seconds to use, but you would need to be prepared for the specific phone model.
Maybe you could even have a CNC machine preloaded with the data for a wide variety of phone models. You put the phone down on the work surface, key in the model, and the CNC machine deftly cuts through the right power lead. Less portable, but would require less precise planning.