Rule 25-3. is headed "WRONG PUTTING GREEN". To the best of my knowledge here is no similar rule for teeing grounds and at my club you play the ball as it lies.

While Rule 25 - 3 b. states "he must not play the ball as it lies", frankly I don't know about shared greens. I don't believe there is any rule saying you must use a specific club, eg. putter, on any part of the course.