My guess is you're talking about a longer-term injury. It has happened. WifS explained it as he hurt his arm in his last outing and the medical diagnosis came days later. I doubt that's the case, seems pretty deep, but it does mirror real-life. A guy pitches, his arm is sore, maybe he skips a start and then the team sends him for a MRI. He's diagnosed with a torn rotator 8 days after his last appearance.