In ICS, an event on "Nov 1" starts on "2016-11-01" and ends on "2016-11-02".
This is convenient for computers, but this isn't what users expect to enter in date controls. They expect to enter "nov 1" to "Nov 1" for a one-day, all-day event. This is consistent with other applications.
Store the value the user entered, but treat it as the first second of the next day when actually using it if the event is an all day event.