Phone OSes should allow the user to exercise plausible deniability by having dual or multiple passwords or other physical means of telling the phone to unlock only in a safe mode that will reveal innocuous documents or photos, job, relatives and friends contacts, and possibly let the inbox and outbox contain only conversations from clean numbers. If a cop signals to pull over, a short bossa nova tap on the phone case might get detected by the accelerometer and trigger that safe mode, until the user tells the phone the emergency is over by tapping a pataflafla followed by a paradiddle diddle (just kidding, but you get the point:^)
Not that I condone any illegal use of cellphones, but often a wrong assumption by a police officer paired by his perceived omnipotence can easily escalate to a level much worse than the "crimes" they intended to prevent.