On this part, I assume it makes a difference whether that ligament will grow back without surgery, or if they'll have to mend it. It would seem this is a fairly important function in life, to be able to use your thumb.
On a related note, I cut the tendon on the outside of my pinky finger clean through with a hedge cutter several years ago now. This is the tendon on either side of the joint that keeps the finger straight when it bends. I can bend my pinky at the last knuckle, sideways about 45 degrees without feeling anything. I opted to not repair it, but the doctor said if I played piano or something, I might want to.
A pinky's not as important as a thumb. :~\
Only if it's not your pinky! ;o)