Blues; what you and K Williams suffered was a rupture of the extensor tendon where it attaches to the distal phalanx. This means, as you so accurately described, Blues, that you cannot extend the finger at the most distal joint (nearest the fingernail). This causes the finger to remain in flexion at that joint, resembling a mallet. This is the common name for this condition, mallet finger deformity.
This is usually a closed injury, caused by jamming the finger hard into something unyielding, and rupturing the tendon as the DIP (Distal Inter Phalangeal) joint is forcefully flexed.
Despite what the doctor told you, Blues, this condition usually does NOT require surgery. Splinting the finger for 8 to 10 weeks will allow the tendon to heal. The trick is that the finger must NEVER be allowed to bend (flex) at the DIP joint, or the tendon ruptures anew. I handled dozens of these over the years, and told people to take off the splint while in the shower, but to take the thumb of the hand where the injury was, and hold it against the injured finger, in slight hyper extension.
Mr. Williams; unfortunately, after several months, the joint tends to become frozen in position, and surgical repair isn't possible. Of course, the orthopods are always coming up with new techniques, so you may wish to consult one who undoubtedly knows more than I.
Tuff; I congratulate you on a most mature and responsible reply. Sometimes even good advice is poorly received. Even by one's own children <grin>. Of course, this happens less as the children grow older; as the saying goes, the older you get, the smarter you think your parents are! Good luck to you, and I hope your finger surgery goes well. Feel free to e-mail me if you have any questions. Walt