I understand your concern....
Most of the time, it is ok to have ground beef (like in a hamburger) a little pink, but to be safe, it is best for it to be thoroughly cooked.
The difference between a medium steak and a medium burger is this basic point....
A medium steak, while pink inside, is usually perfectly safe. Bacteria haven't gotten to the inside of the steak. Hamburger, however, since it is ground up meat, may have bacterial contamination from the grinding process, etc. It is safer to eat hamburgers that are thoroughly cooked. If this happens, it is well within your rights as a consumer to send it back to the kitchen and have it cooked thoroughly. (I realize you didn't see it until after you had eaten.)
At this point, I wouldn't worry about your son... most likely he will be ok.