WATERLOO, Ontario—As the BlackBerry smartphone fell steadily further behind app-loaded rivals like the iPhone in recent years, it was time for an unambiguous response from the chief executive's office.

At Research In Motion Ltd., however, that was complicated. The BlackBerry maker had two chief executives. Moreover, their offices were about a 10-minute drive apart. Meetings with both of them present were rare, say former RIM executives and people who dealt with the company.

Many...