It also depends on when the injury occurs. I've had classmates who had problems early, and they were far more likely to just be medically disenrolled. I had a classmate with eye problems that developed in our junior year. He graduated without a commission. He wasn't happy about that, understandably.
In the end, remember it's tax payer money sending you to school. The tax payer doesn't want to pay for 4 years of your college, without a return on that investment.
When ever there's an injury in a sport, whether it be on TV, or in person, from any of the service academies, we had a habit of saying "well there goes that commission". Usually not the case, but sometimes it it.
They injury you're talking about though just requires surgery and recovery, and wouldn't result in losing that commission. People get hurt call the time. Torn ligaments, broken bones, cuts, bruises....all the time, don't worry about it, just go out and have fun!