So are you required to have all the data that's ever been on your device at the time that you cross an international border? Are you required to copy passwords that were never in 1password onto your device before you travel?
EDIT: Another way to put this: Is there an expectation that a border agent could, for example, ask for the password to my bank account? If not, how would there be an expectation that if that used to be on my iPhone it should still be there when I travel?
Are you a citizen? Because if not, the answer to all of this is "whatever the hell border patrol wants". As far as I know, you absolutely could be asked for your bank account password. You wouldn't be, because any agent asking would probably be fired to avoid a media circus, but it's not actually against any rule. Border patrol discretion for non-citizens is almost absolute.
If you are a citizen, it's not clear that anything at all can be demanded, even logging into an account already on the device. It just hasn't been put to an unambiguous court challenge.
This issue seems to be a bit of a geek trap. Yes, border agents have a fair amount of authority. No, you're not required to twist your mind into a pretzel trying to decide whether what you choose to put on your device constitutes hiding the things you left off. If an agent is asking you something as specific as "did you enable travel mode in 1password" you've probably already triggered some suspicion.
Some of the responses on this thread make it sound like there are people who would actually start explaining travel mode unprompted because they arrived at it by some twisted logic about what 'hiding' means.
EDIT: Another way to put this: Is there an expectation that a border agent could, for example, ask for the password to my bank account? If not, how would there be an expectation that if that used to be on my iPhone it should still be there when I travel?