There is a very interesting discussion about this on the TextSecure issue queue: https://github.com/WhisperSystems/TextSecure/issues/127
In other words, if the bad guys with guns coerce Apple to mint them a cert, they could simply replace your known good binary with a crocked one signed with the new key, and your phone will happily run it. Getting that binary onto your phone is an exercise left to the reader, but there are many means, legal and otherwise, that could be employed to make that happen.
If your privacy means your life is on the line, you probably shouldn't be running stock Android or iOS. (And depending on how you feel about basebands, any modern smartphone, period.)
http://www.oss.net/dynamaster/file_archive/100102/0a947a77d7...
In one part, it says:
The greatest material curse to the profession, despite all its advantages, is undoubtably the telephone. It is a constant source of temptation to slackness. And even if you do not use it carelessly yourself, the other fellow, very often will, so in any case, warn him. Always act on the principle that every conversation is listened to, that a call may always give the enemy a line. Naturally, always unplug during confidential conversations. Even better is it to have no phone in your room, or else have it in a box or cupboard.
That's talking about the plane old telephone in the 1960s.
The message I get from it? If your life is on the line, consider not using any electronic communication at all.