They have to convince a court beyond reasonable doubt that you know the password, AFAIK. An extreme example would be pulling the power plug on a computer you're using as the police arrive: you'd be hard pushed to convince a jury beyond reasonable doubt that you don't know it. Of course, shades of gray, etc.
Maybe if you kept a live Linux USB bootable drive plugged in at all times, you could say that you can't access the installed OS...might have a problem with time-stamps and such but that should be fixable
It's odd that you can be required to prove your own innocence beyond reasonable doubt. I would have sworn that it was supposed to work the other way around.
