I just cut my right index finger with an angle grinder (cutting wheel)? (photo)

the cut is about an inch long between on the inside of my first knuckle. the cut is about 5mm wide and 5 mm deep. no injury to tendon or bone. my doctor said that the wound should be left open since stitching it would make my skin to tight to straighten my index finger. Im wondering if this is the right way to treat this? will my scar be 5mm deep? will my finger not be as flexible as it was before?